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

Question

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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 $c$ .

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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 $c$ .

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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 $c$ .

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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 $c$ .

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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

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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

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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