The contrapositive of the statement pattern [ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The contrapositive of a conditional statement $A 	o B$ is defined as $\sim B 	o \sim A$.Given statement: $[p \lor (p 	o q)] 	o (p \land \sim q

Vedclass · Accepted Answer

$(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$

Vedclass · Answer

(D) The contrapositive of a conditional statement $A 	o B$ is defined as $\sim B 	o \sim A$.Given statement: $[p \lor (p 	o q)] 	o (p \land \sim q)$.Here, $A = [p \lor (p 	o q)]$ and $B = (p \land \sim q)$.Step $1$: Find $\sim B = \sim (p \land \sim q) = \sim p \lor \sim (\sim q) = \sim p \lor q$.Step $2$: Find $\sim A = \sim [p \lor (p 	o q)] = \sim p \land \sim (p 	o q)$.Since $\sim (p 	o q) = p \land \sim q$, we have $\sim A = \sim p \land (p \land \sim q)$.Step $3$: Combine to form $\sim B 	o \sim A$, which is $(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$.This matches option $D$.

The contrapositive of the statement pattern $[p \lor (p \to q)] \to (p \land \sim q)$ is

Similar Questions

Write the negation of the following statement:
$\sqrt{2}$ is not a complex number.

Let $p$ and $q$ stand for the statements "$2 \times 4 = 8$" and "$4$ divides $7$" respectively. Then the truth values of the following biconditional statements are:
$(i)$ $p \leftrightarrow q$
$(ii)$ $\sim p \leftrightarrow q$
$(iii)$ $\sim q \leftrightarrow p$
$(iv)$ $\sim p \leftrightarrow \sim q$

The negation of the contrapositive of the statement $(p \lor \sim q) \to (p \land \sim q)$ is

Which one of the following is a tautology?

Write the contrapositive of the following statement:
If you are born in India,then you are a citizen of India.

Vedclass Test Series

Exam Paper Generator

Online Exam Module