The negation of the contrapositive of the sta | vedclass

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

Question

(D) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.Thus, the contrapositive of

Vedclass · Accepted Answer

$(\sim p \lor q) \land (p \lor \sim q)$

Vedclass · Answer

(D) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.Thus, the contrapositive of $S$ is $\sim (p \land \sim q) 	o \sim (p \lor \sim q)$.Using De Morgan's laws, this is $(\sim p \lor q) 	o (\sim p \land q)$.The negation of an implication $P 	o Q$ is $P \land \sim Q$.Here, $P = (\sim p \lor q)$ and $Q = (\sim p \land q)$.Negation $= (\sim p \lor q) \land \sim (\sim p \land q)$.Applying De Morgan's law to the second part: $\sim (\sim p \land q) = (p \lor \sim q)$.Therefore, the negation is $(\sim p \lor q) \land (p \lor \sim q)$.

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

Similar Questions

Consider the following statement patterns:
$A$. $(q \to p) \vee (p \to q)$
$B$. $(\sim p \vee \sim q) \leftrightarrow \sim (p \wedge q)$
$C$. $[(p \vee q) \wedge \sim p] \wedge \sim q$
$D$. $(p \wedge q) \wedge (\sim p \vee \sim q)$
Which of the following is correct?

The symbolic form of the given switching circuit is equivalent to $..........$

The negative of the statement $\sim p \wedge (p \vee q)$ is

The negation of the statement,$\exists x \in A$ such that $x+5 > 8$ is

If the statement $(p$ $\rightarrow q)$ $\rightarrow (q$ $\rightarrow r)$ is false,then the truth values of statements $p, q, r$ respectively,can be-

Vedclass Test Series

Exam Paper Generator

Online Exam Module