Which is the contrapositive of A ⇒ B ? ( a ) B ⇒ A ( b ) ~ B ⇒ A ( c ) ~ B ⇒ ~ A ( d ) ~ A ⇒ ~ B

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b) the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the 8-second period. t 0 2 4 6 8 V 10 15 12 10 16 2. Find the midpoint rule approximation for (a) n = 4 +5 x²dx using n subintervals. 1° 2 (b) n = 8 36 32 28 36 32 28 24 24 20 20 16 16 12 8- 4 1 2 3 4 5 6 12 8 4 1 2 3 4 5 6

= 5 37 A 4 8 0.5 06 9

Consider the following system of equations, Ax=b : x+2y+3z - w = 2 2x4z2w = 3 -x+6y+17z7w = 0 -9x-2y+13z7w = -14 a. Find the solution to the system. Write it as a parametric equation. You can use a computer to do the row reduction. b. What is a geometric description of the solution? Explain how you know. c. Write the solution in vector form? d. What is the solution to the homogeneous system, Ax=0?

Answer 2

Question

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Answer 6

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Answer 7

Chapter A, Problem 1PQ

To determine

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Answer 8

Expert Solution & Answer

Answer to Problem 1PQ

Solution:

Correct option is $(c)$

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

$A \Rightarrow B$ (A conditional statement)

Options are:

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Definition:

The statement $(~ q) \Rightarrow (~ p)$ is called the contrapositive of the statement $p \Rightarrow q$ .

So, the contrapositive of $A \Rightarrow B$ is $(~ B) \Rightarrow (~ A)$

Hence correct option is $c$ .

Answer 12

Ch. A - Prob. 1PQ Ch. A - Prob. 2PQ Ch. A - Prob. 3PQ Ch. A - Prob. 4PQ Ch. A - Prob. 1E Ch. A - Prob. 2E Ch. A - Prob. 3E Ch. A - Prob. 4E Ch. A - Prob. 5E Ch. A - Prob. 6E

Which is the contrapositive of A ⇒ B ? ( a ) B ⇒ A ( b ) ~ B ⇒ A ( c ) ~ B ⇒ ~ A ( d ) ~ A ⇒ ~ B

Concept explainers

Videos

Which is the contrapositive of $A \Rightarrow B$ ?

$(a) B \Rightarrow A (b) ~ B \Rightarrow A$

$(c) ~ B \Rightarrow ~ A (d) ~ A \Rightarrow ~ B$

Answer to Problem 1PQ

Explanation of Solution

Want to see more full solutions like this?

Chapter A Solutions

Which is the contrapositive of A ⇒ B ? ( a ) B ⇒ A ( b ) ~ B ⇒ A ( c ) ~ B ⇒ ~ A ( d ) ~ A ⇒ ~ B

Concept explainers

Videos