Show that (P ∨ Q) ⇒ ¬R) are logically equivalent
Answers
the two statements have the same truth value under all possible truth value assignments to their constituent variables. Therefore, (P ∨ Q) ⇒ ¬R) and ¬P ∧ ¬Q ∧ R are logically equivalent.
how to show two statements are logically equivalent?to show that two statements are logically equivalent, we need to prove that they have the same truth value under all possible truth value assignments to their constituent variables.
First, let's write out the truth table for the statement (P ∨ Q) ⇒ ¬R):
| P | Q | R | (P ∨ Q) ⇒ ¬R |
| F | F | F | T |
| F | F | T | T |
| F | T | F | T |
| F | T | T | T |
| T | F | F | T |
| T | F | T | F |
| T | T | F | F |
| T | T | T | F |
Now let's consider the statement ¬P ∧ ¬Q ∧ R, which is the negation of the original statement:
| P | Q | R | ¬P ∧ ¬Q ∧ R |
| --- | --- | --- | ----------- |
| F | F | F | F |
| F | F | T | F |
| F | T | F | F |
| F | T | T | F |
| T | F | F | F |
| T | F | T | T |
| T | T | F | F |
| T | T | T | F |
We can see that the two statements have the same truth value under all possible truth value assignments to their constituent variables. Therefore, (P ∨ Q) ⇒ ¬R) and ¬P ∧ ¬Q ∧ R are logically equivalent.
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Related Questions
All six digits in the number are even one digit is used twice all other digits are used once the ones digit is 4 times the hundreds digit the tens digit id the difference of the ones digit and hundreds digit the same digit is in the tens place and hundreds thousands place the thousands digit is not zero
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Answer:
rffrefr
Step-by-step explanation:
What type of transformation is shown?
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Answer:
the third one.
Step-by-step explanation:
clockwise rotation of 90*
Answer:
clockwise rotation of 90 degrees
Step-by-step explanation:
Please put me as brainliest answer :)
Maria had $22 to spend on five pencils. After buying them she had $12.
How much did each pencil cost
Answers
Which best represents the commutative property of addition?
Answers
Answer:
25+25+25+25+25...etc
Step-by-step explanation:
Answer: a+b=b+a
Step-by-step explanation: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44
What is the mean of 9, 25, and 53?
3
9
25
29
Answers
Answer:
29
Step-by-step explanation:
9 + 25 + 53
87
87 ÷ 3
29
Answer:
29
Step-by-step explanation:
add all the numbers up and divide by how many numbers there are.
11
One centimetre is 10 millimetres, one litre is 1,000 cubic centimetres. How many cubic
millimetres are there in a litre?
This is a screen shot from the Halfords web site describing a cuboid shaped water carrier.
Halfords Water Carrier - 20 Litres
. Durable water storage carrier with tap
• 20 litre storage capacity
.
•
Measurements-(L) 37.5cm (W) 16cm (H) 28cm
Simple rinse with warm water and washing up liquid prior to first use
(a) Modern specifications require dimensions in millimetres. Convert the dimensions
to millimetres.
(b) The "20 litres" may be incorrect. Use the dimensions given to estimate the
volume of water it holds.
(c) A cubic centimetre of water weighs one gram. Estimate the weight of a full
carrier in Kilograms
JAZZLE
Answers
(a) After Convert the dimensions we get Length: 375 mm Width: 160 mm Height: 280 mm
(b) Calculating the result: Volume = 16,800,000 mm³
(c) The estimated weight of the full carrier is 16,800 kilograms.
(a) To convert the dimensions to millimeters, we simply multiply each dimension by 10, as there are 10 millimeters in a centimeter.
Length: 37.5 cm = 37.5 × 10 mm = 375 mm
Width: 16 cm = 16 × 10 mm = 160 mm
Height: 28 cm = 28 × 10 mm = 280 mm
So, the dimensions in millimeters are:
Length: 375 mm Width: 160 mm Height: 280 mm
(b) To estimate the volume of water the carrier holds, we multiply the dimensions together.
Volume = Length × Width × Height
Volume = 375 mm × 160 mm × 280 mm
Calculating the result: Volume = 16,800,000 mm³
(c) Since 1 liter is equal to 1,000 cubic centimeters, and we know that 1 cubic centimeter of water weighs 1 gram, we can estimate the weight of the full carrier in kilograms.
Weight = Volume × Weight of 1 cubic centimeter of water
Weight = 16,800,000 mm³ × 1 g Weight = 16,800,000 g
To convert grams to kilograms, divide by 1,000:
Weight = 16,800,000 g ÷ 1,000 = 16,800 kg
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Which line is the graph of y = -2 x + 2?
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Step-by-step explanation:
Does this graph help?
ab-c/d has a value of 24. write the values if :-
1- a, b, c, d are all positive.
2- a, b, c, d are all negative.
3- a, b, c, d are mixed of negative and positive.
WRITE ANSWERS FOR 1, 2 AND 3
Answers
The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24
Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.
Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9
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Ella had 3/5 gallon of lemonade in her refrigerator. She drank 1/5 gallon for lunch. How much lemonade does she have left. Which equation could you solve to find n, the amount of lemonade that is left?
Answers
Ella has 2/5 gallons of lemonade left. The value of n is (2/5) gallon for the given equation.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
To determine the amount of lemonade Ella has left after drinking 1/5 gallon for lunch, we can subtract the amount she drank from the original amount she had:
Amount of lemonade left = (3/5) gallon - (1/5) gallon = (2/5) gallon
Therefore, Ella has 2/5 gallons of lemonade left.
We could also write an equation to solve for n, the amount of lemonade that is left:
n = (3/5) gallon - (1/5) gallon
Simplifying the right-hand side:
n = (2/5) gallon
Thus, Ella has 2/5 gallons of lemonade left.
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Graph the line with y-intercept 4 and slope 2.
Answers
Answer is in the file atttached.
There are four drops of red food coloring in
25 candy canes. How much red food
coloring is in each candy cane
Answers
Answer:
0.16 drops
Step-by-step explanation:
If there are a total of 4 drops in 25, the amount in each could be represented as 4/25. This results in 0.16, thus 0.16 drops in each candy cane.
If this helped you understand and find the solution brainliest would be much appreciated :)
Find the standard form of the parabola
with vertex: (- 2,5) and directrix: x = 3.
Answers
Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so
\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}\)
SOMEBODY PLEASE PLEASE HELP ME
ILL GIVE YOU 5 STARS, BRAINLIEST AND GIVE A HEART PLEASE HELP
(Please make sure you answer Part B of the question and show your work!!)
Answers
From the results, the mode of transportation that was faster for June is Bus.
How to determine the fastest trnasportation modeTo obtain the fastest means of transportation, the mode of the figures will provide a clue. For Bus, the figures are 16, 14, 15, 14, 31, 15 and for walking, the figures are 22, 19, 21, 20, 21, 20.
The highest nmbers in occurence for the first set of figures are 14 and 15 and for the second set of figures, the numbers that appeared most are 20, 21, and 22. So, the bus offered the fastest route for going to school.
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The manager of a grocery store wants to determine what proportion of people who enter
his store are his regular customers. What size sample should he take so that at 95%
confidence the margin of error will not be more than 0.1?
Answers
answer:
74
Step-by-step explanation:
The sample size for the given confidence interval is 96.
What is a confidence interval?A range of estimates for an unknown parameter is called a confidence interval (CI). A confidence level calculates a confidence interval; The most common confidence level is 95 percent. The confidence level is the percentage of corresponding CIs that contains the actual value of the parameter over time.
Given confidence of margin is at 95%
E = 0.1 = margin of error
95% confidence interval of Z = 1.96
sample size = n, which is given by
n = (Z/E)²(p)(1 - p)
n = (1.96/0.1)²(0.5)(0.5)
n = 96.04 = 96 approx
Hence, the sample size is 96.
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the perimeter of a parallelogram ABCD is 78cm. AD is 3cm more than twice AB. Find the length of all four sides of ABCD
Answers
Answer:
AB=12 AD= 27
Step-by-step explanation:
If 32^2C = 8^C+7, what is the value of c?
1
2
3
5
Answers
32 = 2⁵ and 8 = 2³, so you can rewrite the equation as
\(32^{2c}=8^{c+7}\implies(2^5)^{2c}=(2^3)^{c+7}\implies 2^{10c}=2^{3c+21}\)
The bases of both sides are equal, so the exponents must be too. Solve for c :
10c = 3c + 21
7c = 21
c = 3
Which expression is equivalent to 15 n=10 (n+3/n)?
Answers
Answer:
±√6
Step-by-step explanation:
\(15n=10(n+\frac{3}{n} )\) is your expression first muiltiply out the 10 to get 15n= 10n+10 3/n next subtract 10 n from both sides to get 5n=10+3/n multiply both sides by n to get 5n^2=13 combine both sides and use the quadratic equation to solve to get your solution of ±√6
Find the average rate of change of f(x) = x°-2x² +3+ 3x from x=1 to x=3.Simplify your answer as much as possible.
Answers
The average rate of change for a function f(x) from x=a to x=b is:
\(\frac{f(b)-f(a)}{b-a}\)For the given function:
\(f(x)=x^3-2x^2+3x\)Averate rate of change from x=1 to x=3:
\(\begin{gathered} \frac{f(3)-f(1)}{3-1}=\frac{(3^3-2(3)^2+3(3))-(1^3-2(1)^2+3(1))}{3-1} \\ \\ =\frac{(27-2(9)+9)-(1-2+3)}{2} \\ \\ =\frac{(27-18+9)-(2)}{2} \\ \\ =\frac{18-2}{2} \\ \\ =\frac{16}{2} \\ \\ =8 \end{gathered}\)Then, the averate rate of change for the given function from x=1 to x=3 is 8
Which of the following shapes has exactly 1 line of symmetry?
Answers
Answer:
Isosceles triangle is the shape which has exactly one line of symmetry.
a rectangle auditorium seats 1428 people. The number of seats in each row exceeds the number of rows by 8. Find the number of seats in each row
Answers
Let, the number of rows be=x
Then the number of seats in each row will be=x+8
Then the equation will be:
x(x+8)=1428
x*x+8x-1428=0
On solving(use your calculator) the values of x=34,-42
Since the number of rows cannot be negative we take positive number which is x=34
Then the number of seats in each row=34+8=42 which is the required answer
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BRAINLIEST!!!! AND 100
POINTS!!!
Answers
The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics.
What is 3D and 2D ?The terms 2D and 3D describe the precise sizes of a computer workstation. Using the horizontal and vertical (X and Y) axes, 2D is "flat," meaning that there are only two dimensions to the picture, which becomes a line when rotated to the side. The depth (Z) dimension is added in 3D.A two-dimensional form known as a "2D shape" is characterised by its horizontal and vertical axes (x-axis and y-axis)The three spatial dimensions of width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.The rectangle, square, circle, triangle, and any other polygon are a few examples of 2D forms. Cuboid, cube, sphere, cone, prism, cylinder, pyramid, etc. are a few examples of 3D forms.Fill in blanks :
A point has no dimension. it is an abstract idea of a location in space.
A vertex is where two edges meet at a point
A line has edge dimension - length . An edge is a line segment where two faces meet.
A flat plane figures has a 2 dimension - length and width
The 3 points of a 3D object is a plane.
Three dimensional objects have vertices, edges and faces unless they are the geometric solids like cylinders, cones and sphere.
when we talk about line we are looking at the measure of a one dimensional figure.
when we talk about area we are looking at the space inside of a two dimensional figure.
when we talk about volume we are looking at the total space enclosed by a three dimensional figure.
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Please give me the correct answer.
Answers
Answer:
subtract 40 from both sides
Answer:
You subtract 40 which will equal -6 and now you divide -6/4n and the answer is n=-1.5
Step-by-step explanation:
need help on this question
Answers
Did you say nevermind so I will just take these free points
Will mark brainlist and give extra points bth grade math
Answers
Answer:
the answer is d
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
Stacey earned $100 for 4 hour plus 20 every additional hour babysitting on Saturday.She earned at most $160 in all.a)Write an inequality that represents how much Stacey worked on Saturday.
Answers
Let x be the number of hours stacey worked on Saturday.
For hte first 4 hours, she earned $100 and $20 every additional hour.
Since her total hours is x, we will subtract 4 from it and that will be the number of hours she worked for $20
\(100+20(x-4)\)She earned at most $160, equating the expression above less than or equal to 160.
\(\begin{gathered} 100+20(x-4)\le160 \\ 20(x-4)\le160-100 \\ 20x-80\le60 \\ 20x\le60+80 \\ 20x\le140 \\ x\le\frac{140}{20} \\ x\le7 \end{gathered}\)Her total number of hours will be x ≤ 7
Since Stacey needs to work at most 7 hours to get $160
The number of hours she will need is 7 hours
Let's check.
Subsitute x = 7 to the expression above :
\(\begin{gathered} 100+20(x-4) \\ \Rightarrow100+20(7-4) \\ \Rightarrow100+20(3) \\ \Rightarrow100+60 \\ \Rightarrow160 \end{gathered}\)Therefore, the answer is correct.
PLS HELP!!
Given the diagram below, find the value of x.
The value of x is
Answers
Answer:
44°
Step-by-step explanation:
180-30-14=136
180-136
44
What is x if x=1+2+3+4..............
Answers
Answer:
If x is equal to the sum of the series 1+2+3+4, then the value of x is 10.
The sum of the series 1+2+3+4 is calculated by adding each term in the series:
1 + 2 + 3 + 4 = 10
So, x = 10.
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
It is not possible to determine the value of x without knowing the upper limit of the series of numbers being added together. If the series of numbers being added together is finite, then x can be calculated by adding up all of the numbers in the series.
For example, if x is equal to the sum of the first ten positive integers (1+2+3+4+5+6+7+8+9+10), then x would be equal to 55.
To find the sum of the first n positive integers, you can use the formula:
x = (n * (n + 1)) / 2
where n is the number of integers in the series. For example, if n is equal to 4, then the formula would be:
x = (4 * (4 + 1)) / 2 = (4 * 5) / 2 = 20 / 2 = 10
This formula can be used to quickly and easily calculate the sum of the first n positive integers for any value of n.
Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is):
Multiple Choice
$1,350
$1,535.21
$1,653
$5,163
Answers
The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).
Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.
Assuming a semiannual compounding rate of 8%,
As per the given information, the required solution would be as:
Amount to be paid into the fund each semi-annual period will be
= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))
= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))
= $1535.21
Thus, the required amount to be paid into the fund each period is $1535.21.
Hence, the correct answer would be an option (B).
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IXL problem please help
……………………
Answers
Find the midpoint of (9,2) and (-7,-9)
Answers
Answer:
(1,-7/2)
Step-by-step explanation:
The midpoint of (9,2)(-7,-9) is (1,-7/2)