The negation of p rightarrow (sim p vee q) is | vedclass

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

Question

(D) To find the negation of $p \rightarrow (\sim p \vee q)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$.Here,$A = p$

Vedclass · Accepted Answer

$p \wedge \sim q$

Vedclass · Answer

(D) To find the negation of $p \rightarrow (\sim p \vee q)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$.Here,$A = p$ and $B = (\sim p \vee q)$.Therefore,$\sim[p \rightarrow (\sim p \vee q)] \equiv p \wedge \sim(\sim p \vee q)$.Using De Morgan's Law,$\sim(\sim p \vee q) \equiv \sim(\sim p) \wedge \sim q \equiv p \wedge \sim q$.Substituting this back,we get $p \wedge (p \wedge \sim q)$.Since $p \wedge p \equiv p$,the expression simplifies to $p \wedge \sim q$.Thus,the negation is $p \wedge \sim q$.

The negation of $p \rightarrow (\sim p \vee q)$ is

Similar Questions

The statement pattern $\sim(p \leftrightarrow \sim q)$ is

What is the identity element for the sum (disjunction) in Boolean algebra of logical statements?

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :

If the truth value of the statement pattern $( \sim p \land q) \lor ( \sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

The statement $(p \wedge q) \to (p \vee q)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module