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

Don't use ai to answer I will report you answer

find three soultion independed by lagrang 2x (y + z²)p + y(2y + z²)q = Z³

by Lagrange theorme find (4) Soultions independed for: 2x (y + z²) P + Y (29 +2²) q = 23

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