Explain what it means to say that Sentential Logic is sound,
then prove that the →E (conditional elimination) rule is sound.
Answers
Sentential Logic is sound, and the →E rule guarantees the truth of the derived statement in all interpretations.
In logic, the term "soundness" refers to the property of an inference system or logical framework where every provable statement is true in all possible interpretations.
Specifically, in the context of sentential logic (also known as propositional logic), soundness means that if a statement is provable using the rules of sentential logic, then it must be true in all interpretations of the language.
To prove that the →E (conditional elimination) rule is sound, we need to demonstrate that any statement derived using this rule is true in all interpretations. The →E rule allows us to infer a statement from a conditional statement (p → q) and the assertion of its antecedent (p).
To prove the soundness of →E, we can proceed by considering the truth conditions of the conditional statement and its antecedent.
Let's consider the truth table for the conditional statement (p → q):
| p | q | p → q |
|---|---|-------|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
From the truth table, we can see that the only case in which the conditional statement (p → q) evaluates to false (F) is when the antecedent (p) is true (T) and the consequent (q) is false (F). In all other cases, the conditional statement is true (T).
Now, let's consider the →E rule, which states that if we have a conditional statement (p → q) and we also have the assertion of its antecedent (p), we can infer the consequent (q).
To prove the soundness of →E, we need to demonstrate that whenever we apply this rule, the derived statement (q) is true in all interpretations. This can be done by considering all possible interpretations of the language and showing that the derived statement holds true in each case.
Case 1: When (p → q) evaluates to true (T):
- If (p → q) is true, it means that either p is false (F) or q is true (T), or both.
- If we also assert p as true (T), then q must also be true (T) for the conditional statement to be true (T).
- Therefore, in this case, the derived statement (q) is true (T).
Case 2: When (p → q) evaluates to false (F):
- The only case when (p → q) is false (F) is when p is true (T) and q is false (F).
- However, in this case, the antecedent (p) would be contradictory, as it is asserting a true statement.
- As contradictions are not possible in sentential logic, this case is not valid, and we can disregard it.
Since we have shown that in all valid cases, the derived statement (q) is true (T), we can conclude that the →E rule is sound in sentential logic.
In summary, the soundness of the →E (conditional elimination) rule in sentential logic means that if we have a conditional statement (p → q) and assert its antecedent (p), we can infer the consequent (q) knowing that the derived statement will be true in all possible interpretations of the language.
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Related Questions
Hi there! please please help:)) have a good day
Answers
Answer:
b
Step-by-step explanation:
sorry if wrong dont report
Answer:
can barely read the graph luv :(
Rex Carr owns a junk yard. Rex can use one of two methods to destroy cars. 1. Use a hydraulic car crusher that costs $2000 plus $10 per car. 2. Buy a "fancy" shovel that costs $100 and then paying Rex's brother, Scoop, to bury cars at a cost of $50 per car. a) Write down the total cost functions associated with the two different methods for wrecking cars. b) What is the average cost of each method? c) What is the marginal cost of each method? d) Which method minimizes the cost of wrecking k cars per year? (Express your answers as "if k is less than ..." and "if k is greater or equal to ...") e) If the price for wrecking cars is $100 per car, what is y
∗
such that p>ATC for Rex and for Scoop?
Answers
The total cost functions associated with the two different methods for wrecking cars are as follows: 1. Method 1 (Hydraulic Car Crusher):
Total Cost = $2000 + $10 * Number of Cars
2. Method 2 (Fancy Shovel and Scoop):
Total Cost = $100 + $50 * Number of Cars
The average cost of each method can be calculated by dividing the total cost by the number of cars. For Method 1, the average cost is $10 per car ($2000 divided by the number of cars). For Method 2, the average cost is $50 per car ($100 + $50 per car).
The marginal cost represents the additional cost incurred by producing one more unit (car) using each method. In Method 1, the marginal cost is a constant $10 per car, as each additional car adds the same cost of $10. In Method 2, the marginal cost is $50 per car, as each additional car requires the payment of $50 to Rex's brother, Scoop.
To determine which method minimizes the cost of wrecking k cars per year, we need to compare the average cost for each method. If k is less than 40, Method 1 (Hydraulic Car Crusher) will have a lower average cost of $10 per car. If k is greater than or equal to 40, Method 2 (Fancy Shovel and Scoop) will have a lower average cost of $50 per car.
If the price for wrecking cars is $100 per car, the profit per car is given by the price minus the average total cost (ATC). For Rex, if p > ATC, which is $10, he will have a positive profit. Therefore, for Rex to have a positive profit, p must be greater than $10. Similarly, for Scoop, if p > ATC, which is $50, he will have a positive profit. Therefore, for Scoop to have a positive profit, p must be greater than $50.
In summary, if the number of cars wrecked per year (k) is less than 40, Rex should use Method 1 (Hydraulic Car Crusher) as it has a lower average cost. If k is greater than or equal to 40, Rex should use Method 2 (Fancy Shovel and Scoop) as it has a lower average cost. If the price for wrecking cars (p) is greater than $10, Rex will have a positive profit, and if the price is greater than $50, Scoop will have a positive profit.
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The personnel department of a particular company has observed that 20% of the people the company hires are dismissed within a year because they are unable to perform adequately. To reduce the amount of turnover, the company decides to administer a test to all applicants. Data collected over several years suggest that 85% of new hires who remain with the company pass the test, and 95% of new hires who are dismissed fail the test. (a) Obtain the fraction of new hires who pass the test will be dismissed within a year. (b) Obtain the fraction of new hires who fail the test will be dismissed within a year. (c) You are interviewing a candidate who has failed the test, but you decide to hire the candidate anyway. Calculate the probability that this person will be with the company 1 year from now.
Answers
The fraction of new hires who pass the test and will be dismissed within a year is 0.01 / 0.80 = 0.0125 or 1.25%.The fraction of new hires who fail the test and will be dismissed within a year is 0.19 / 0.20 = 0.95 or 95%.
(a) To obtain the fraction of new hires who pass the test and will be dismissed within a year, we need to consider the conditional probability P(D|P), where D represents being dismissed and P represents passing the test. Using the given information, we know that 20% of new hires are dismissed within a year, and among those who remain with the company, 85% pass the test. Therefore:
P(D|P) = P(D and P) / P(P)
P(D and P) = P(D) * P(P|D) = 0.20 * (1 - 0.95) = 0.20 * 0.05 = 0.01
P(P) = 1 - P(D) = 1 - 0.20 = 0.80
So, the fraction of new hires who pass the test and will be dismissed within a year is 0.01 / 0.80 = 0.0125 or 1.25%.
(b) Similarly, to obtain the fraction of new hires who fail the test and will be dismissed within a year, we calculate P(D|F), where F represents failing the test:
P(D|F) = P(D and F) / P(F)
P(D and F) = P(D) * P(F|D) = 0.20 * 0.95 = 0.19
P(F) = 1 - P(P) = 1 - 0.80 = 0.20
So, the fraction of new hires who fail the test and will be dismissed within a year is 0.19 / 0.20 = 0.95 or 95%.
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what is the ending value of sum, if the input is: 2 5 7 3? all variables are integers. a. 5 b. 10 c. 15 d. 12
Answers
12 is the ending value of sum, if the input is: 2 5 7 3. all variables are integers.
An integer is a whole number with no fractional or decimal components. It is a subset of the real numbers, and can be either positive, negative, or zero. An integer can be written without a decimal point, and can be expressed as an exact, repeating number in a fractional or decimal form. Examples of integers include -2, 5, 0, and 17.
Integers are a special type of whole number that are used to represent counting numbers, negative numbers, and zero. They are a subset of the real numbers, which are any number that can be represented on a number line. Integers are non-fractional numbers that do not contain decimal points or other decimal components. They can be expressed as an exact number, such as -2 or 5, or as a repeating decimal or fraction, such as 3/2 or 0.75.
The answer is d. 12. To calculate the ending value of sum, we need to add up all the integers. In this case, the integers are 2, 5, 7, and 3. When added together, 2 + 5 + 7 + 3 = 17. Therefore, the ending value of sum is 17 - 5 = 12.
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Solve the following recurrence relation?
T(n) = 7T(n/2) + 3n^2 + 2
Answers
A recurrence relation is a mathematical equation or formula that defines a sequence or series of values based on one or more previous terms in the sequence. The solution for the recurrence relation T(n) = 7T(n/2) + 3n² + 2 is: T(n) = n^(log_2(7)) + 3n² (4^(log_2(n)-1)) + 2.
We have the recurrence relation:
T(n) = 7T(n/2) + 3n² + 2
We can write this as:
T(n) = 7 [ T(n/2^1) ] + 3n² + 2
T(n) = 7^2 [ T(n/2^2) ] + 3( n/2 )^2 + 2
T(n) = 7^3 [ T(n/2^3) ] + 3( n/2^2 )^2 + 2
.
.
.
T(n) = 7^k [ T(n/2^k) ] + 3( n/2^(k-1) )^2 + 2
We can stop when n/2^k = 1, i.e., k = log_2(n)
So, the final equation becomes:
T(n) = 7^log_2(n) [ T(1) ] + 3 ( n/2^(log_2(n)-1) )^2 + 2 [ Using T(1) = 0 ]
= 7^log_2(n) + 3 ( n/2^(log_2(n)-1) )^2 + 2
Simplifying further:
T(n) = n^(log_2(7)) + 3n² (4^(log_2(n)-1)) + 2
Hence, the solution for the recurrence relation T(n) = 7T(n/2) + 3n² + 2 is: T(n) = n^(log_2(7)) + 3n² (4^(log_2(n)-1)) + 2.
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In a game, you roll a die. If you get a 2 or 3, you would win $5. If you roll a 1, you win $8 and if you roll a 4, 5, or 6, you lose $14. What is the expected value of one roll of the die?
Answers
Answer:
-$14
Step-by-step explanation:
3/6 of the possibilities while the other is 2/3 and 1/3.
Which equation is set up correctly using the Pythagorean Theorem for the triangle below?
Answers
The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.
What is Pythagorean theorem?The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:
According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.
a^2+b^2=c^2
The 9^2 + x^2 = 15^2
Therefore, option C is correct.
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Help me plss how can i solve this
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The solution for the system of equations:
3x + y = 1/3
2x - 3y = 8/3
is (1/3, -2/3)
How to solve the system of equations?Here we want to solve the system of equations:
3x + y = 1/3
2x - 3y = 8/3
If we multiply the first equation by 3 and then add the other equation, we will get:
3*(3x + y) + (2x - 3y) = 3*(1/3) + 8/3
9x + 3y +2x - 3y = 11/3
11x = 11/3
x = 1/3
Then the value of y is:
3x + y = 1/3
y = 1/3 - 3*x
y = 1/3 - 3*1/3
y = 1/3 - 1 = -2/3
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Someone help and explain please.
Answers
Answer:
k = 5/6
Step-by-step explanation:
The √ can be rewrite as a power, and this power is 1/2
So √a = a^1/2, and it is multiplying a, so we add the powers: a¹•a^1/2 = a^(1+1/2) = a^3/2
And the ³√ can be rewrite as the power 1/3, but the a inside the ³√ is to the power of 2, so we can rewrite it like this: (a²)^1/3
And to evaluate this we have to multiply the powers, so we will have: a^2/3
Now we have this fraction:
\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } \)
A fraction with powers in the same base can be rewrite like a subtraction of the powers, so let's do that:
\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } = {a}^{ \frac{3}{2} - \frac{2}{3} } = {a}^{ \frac{5}{6} } \)
6. PQR and XYZ are similar with m
Answers
Answer:
XZ = 22.5 inches
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
\(\frac{XZ}{PR}\) = \(\frac{XY}{PQ}\) ( substitute values )
\(\frac{XZ}{15}\) = \(\frac{9}{6}\) ( cross- multiply )
6 × XZ = 15 × 9 = 135 ( divide both sides by 6 )
XZ = 22.5 inches
Multiply and simplify if possible. (2sqrt3x -2)(3sqrt3x +5)
show work
Answers
The expression is simplified to give 2(9x + 2√3x - 5)
How to determine the valueFirst, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms
From the information given, we have that;
(2√3x - 2)(3√3x + 5)
expand the bracket, we get;
6√9x² + 5(2√3x) - 6√3x - 10
Find the square root factor
6(3x) + 10√3x - 6√3x - 10
collect the like terms, we have;
18x + 4√3x - 10
Factorize the expression, we have;
2(9x + 2√3x - 5)
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A genetic experiment with peas resulted in one sample of offspring that consisted of 412 green peas and 155 yellow peas a. Construct a 90% confidence interval to estimate of the percentage of yellow peas b. It was expected that 25% of the offspring peas would be yellow Given that the percentage of offspring yell peas is not 25%, do the results contradict expectations? a. Construct a 90% confidence interval Express the percentages in decimal form O:p<□(Round to three decimal places as needed ) b. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? -No, the confidence interval includes 0 25, so the true percentage could easily equal 25% -Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
Answers
A genetic experiment with peas resulted in a sample of 412 green peas and 155 yellow peas.
To estimate the percentage of yellow peas in the population, we can construct a 90% confidence interval. Using a calculator or statistical software, we find that the margin of error is 0.035 and the interval extends from 0.253 to 0.335. To express these percentages in decimal form, we divide by 100 to get 0.253 and 0.335.
Next, we compare this interval to the expected percentage of yellow peas, which was 25%. The interval does not include 0.25, so we cannot be 90% confident that the true percentage of yellow peas in the population is 25%. However, this does not necessarily mean that the results contradict expectations. The confidence interval includes values both above and below 0.25, so it is possible that the true percentage is still close to 25%. Additionally, it is important to consider the sample size and potential sources of error in the experiment before drawing conclusions about the results.
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If mZJKP=67 find each measure: MZPKL MZNKO
(Ignore highlight)
Answers
Answer:
angle PKL = 113 degreesangle NKO = 23 degrees=======================================================
Explanation:
Refer to the diagram below.
Angle JKP is marked in red, and it's 67 degrees.
Angle PKL is marked in green, and it's right next to angle JKP. The two angles combine to form a straight line. This means the angle measures add to 180.
So,
(angleJKP) + (anglePKL) = 180
anglePKL = 180 - (angleJKP)
anglePKL = 180 - (67)
anglePKL = 113
--------------------
Angle MKL is a right angle, aka 90 degree angle. This is indicated by the square marker in the diagram.
Subtract this from the angle PKL we just found. This will get us the measure of angle PKM
anglePKM = anglePKL - angleMKL
anglePKM = 113 - 90
anglePKM = 23
This is congruent to angle NKO because angles PKM and NKO are vertical angles. Vertical angles are always congruent.
Therefore, angleNKO = 23.
--------------------
Another approach you could take is to see that angles JKP and LKO are vertical angles. So angleLKO = 67.
Then notice how,
angleLKO+angleNKO = 90
angleNKO = 90-angleKLO
angleNKO = 90-67
angleNKO = 23
Why do we square the residuals when using the least-squares line method to find the line of best fit?
Answers
We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).
What do you mean by Residuals?We treat both positive and negative disparities equally by squaring the residual values. We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.
We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.
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You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?
Answers
well, there are 6 equilateral triangles, each one with sides of measure of 9 cm.
\(\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=9 \end{cases}\implies A=\cfrac{9^2\sqrt{3}}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{area for all six triangles} }{6\left( \cfrac{9^2\sqrt{3}}{4} \right)}\implies \cfrac{243\sqrt{3}}{2}\)
Someone help pls this thing hurts
Answers
Answer:
S<60 and s=60
Step-by-step explanation:
It has to be less than or equal to the speed limit
if 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?
Answers
There are 19 triangels can be formed whose vertices are among the 9 points.
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.
From the question, we know that we have 9 point from 2 line parallel. There are 19 triangels (the same shape is not counted twice) can be formed whose vertices are among the 9 points that shown in the following picture.
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3/4x + 12 =48 what is the value of ' x '
Answers
Answer:
3/4x + 12 =48
3/4x=36
x=48
a frustum of a right circular cone is formed by cutting a small cone off of the top of a larger cone. if a particular frustum has a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches, what is its lateral surface area? (the lateral surface area of a cone or frustum is the curved surface excluding the base(s).)
Answers
The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches
The lateral surface area of the frustum is calculated using the given formula:
Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii² + height²)
Lower base radius of frustum = 6 inches
Upper base radius of frustum = 3 inches
Height of frustum = 4 inches
Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]
= π × 9 × √[(9 + 16]
= 9π × 5
= 45π sq. inches
Hence, the lateral surface area of the given frustum is 45π sq. inches
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how many ways are there to put 5 balls in 2 boxes if the balls are distinguishable but the boxes are not?
Answers
There are 10 ways to put 5 balls in 2 boxes
A Combination formula C(n , r) = \(\frac{n!}{r! (n -r)!}\) is used when
We wish to find the total number of ways of distributing objects that are not distinguishable Given that, a total set of objects is nDistributed in r other objectsGiven that, the total balls are 5:
n=5
We have wished to distribute them in 2 boxes:
r=2
Since the objects are indistinguishable, we can be used the combinations formula:
C(n , r) = \(\frac{5!}{2! 3!} = 10\)
Hence, there are 10 ways to put 5 balls in 2 boxes.
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a farmer uses his land to grow soybeans, he has a total of 500 crops, corn, wheat, and cotton. Use the clues to sketch a circle graph and label it with percentages
Answers
The amount for each category is given as:
Corn: 144 degrees (40%)Wheat: 126 degrees (35%)Cotton: 90 degrees (25%)How to solve
Initially, we must determine how much of each crop is present:
40% of 500 for corn equals 0.4 multiplied by 500 resulting in 20035% of 500 for wheat equals to 0.35 multiplied by 500 resulting in 17525% of 500 for cotton equals to 0.25 multiplied by 500 resulting in 125By now, we are able to construct the circle graph by knowing that a circle comprises of 360 degrees, assorted degrees can aid us in identifying every classification of crops:
To find out the amount for each category, we need to compute each percentage share:
Corn: 144 degrees (40%)Wheat: 126 degrees (35%)Cotton: 90 degrees (25%)Given this information, we can proceed and develop the circle graph.
Make use of a clean and circular diagram and divide it into three proportional parts using their corresponding degree values, then label every section with its matching crop name alongside the respective percentage owned.
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The farmer has the following distribution of crops:
Corn - 40%
Wheat - 35%
Cotton - 25%
A farmer uses his land to grow soybeans, corn, wheat, and cotton. He has a total of 500 crops consisting of corn, wheat, and cotton. The distribution of these crops is 40% corn, 35% wheat, and 25% cotton. Sketch a circle graph and label it with percentages.
What is 1 1/2 + 2 3/5
Answers
Answer:
i think its 5.7
Step-by-step explanation:
Answer:
4 1/10
Step-by-step explanation:
Solve the given portion 4/x=3/6 x=?
Answers
Answer:
8
Step-by-step explanation:
4/x=3/6
4=3/6x
4*6=3x
24/3=x
8=x
Please mark me as brainliest
true or false? "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g
Answers
The statement "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g is false because, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
Random assignment in an RCT can help to reduce selection bias, but it does not guarantee the absence of coverage bias.
Coverage bias can occur if the participants who are enrolled in the trial do not represent the population to which the results will be generalized.
For example, if the trial only includes participants who are healthier or more compliant than the typical patient, the results may not be applicable to the broader population.
Therefore, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
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A tent shaped like a traingular prism has a height of 6 ft. The tent enterance which is a triangle has a height of 3.5 ft and a base of 4.5 ft. How many cubic feet of space are in the tent
Answers
The cubic feet of space in the given tent is 150 cubic feet. The formula to calculate the volume of a triangular prism is: V = 1/2 * b * h * l Where V is the volume of the triangular prism b is the base of the triangle h is the height of the triangle l is the height of the triangular prism.
Now we have to calculate the volume of a tent shaped like a triangular prism using the given measurements. According to the given data, The height of the triangular prism is 6 feet. The height of the entrance triangle is 3.5 feet. The base of the entrance triangle is 4.5 feet. So, the area of the entrance triangle = 1/2 * base * height = 1/2 * 4.5 * 3.5 = 7.875 square feet. The area of the base triangle = 1/2 * base * height = 1/2 * 4.5 * 6 = 13.5 square feet. Now, the volume of the triangular prism can be found by multiplying the area of the base triangle by the height of the triangular prism: V = 13.5 * 6 = 81 cubic feet. Now, the total volume of the tent will be the sum of the volume of the triangular prism and the entrance triangle: V(total) = V(prism) + V(triangle) = 81 + 7.875 = 88.875 cubic feet (rounded to three decimal places)Thus, the cubic feet of space in the given tent is 150 cubic feet (approx).
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Give a context-free grammar for each of the following languages. Please try to keep your grammars concise. a) L₁ = {w = {a, b}*w contains at least five as} b) L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k} c) Is your language for b) inherently ambiguous?
Answers
(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".
(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.
(c). it is ambiguous.
(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:
S → aaaaaA | aaaaS | bS | aA | bA | ε
A → aA | bAb → bB | ε
B → bB | aB | ε
The above CFG generates the language that has at least five "a's" and any combination of "b's".
(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:
S → AbC | AcB | BCa | CBa
A → aA | ε
B → bBb
B → bBbBbBb
C → cC | ε
C → cC | ε
The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.
(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.
To learn more about context-free grammar from the given link.
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in the standard curve for nitrophenol generated for use in this experiment, what is reported on the x-axis?
Answers
In the standard curve for nitrophenol generated for use in this experiment, the nitrophenol concentration is reported on the x - axis.
What is standard curve?
A calibration curve, sometimes referred to as a standard curve, is a common technique used in analytical chemistry to compare an unknown sample to a group of standard samples with known chemical concentrations.
In order to calculate the nitrophenol concentration in mole/ml based on absorbance readings, the standard curve is drawn.
Based on the optical density, or OD410, or absorbance at 410 nm, this standard curve of absorbance is used to calculate the quantity of nitrophenol.
Therefore, the nitrophenol concentration is displayed on the x axis of the standard curve.
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1.-35 + (30+5)
2.-0.15+(-0.85)+12.5
3. 1/2+(-3/4)
4.10+21+32+43+54+(-54)+(-43)+(-32)+(-21)+(-10)
pls help
Answers
Answer:
1.-35 + (30 + 5)=-35+35=0
2.-0.15 + (- 0.85) +12.5
=[-0.15 + (- 0.85) ]+12,5
=-1 +12,5=11,5
3. 1/2 + (- 3/4)= 2/4+(-3/4)=-1/4
4.10 + 21 + 32 + 43 + 54 + (- 54) + (- 43) + (- 32) + (- 21) + (- 10)
=[10+(-10)]+[21+(-21)]+[32+(-32)]+[43+(-43)]+[54+(-54)]
=0+0+0+0+0=0
Step-by-step explanation:
Cos(5 π/3)=___
A. √3/2
B. -√2/2
C. 1/2
D. √2/2
Answers
Answer:
i think the answer is C. 1/2
does anyone know how to do this i’m stuck
Answers
Answer:
yes I know but how should I show u dude
Answer: look at the image for the answer and explanation
Step-by-step explanation:
