The negation of (p wedge q) rightarrow (sim p | vedclass

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

Question

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

Vedclass · Accepted Answer

$p \wedge q \wedge (\sim r)$

Vedclass · Answer

(D) To find the negation of the implication $(p \wedge q) \rightarrow (\sim p \vee r)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$. Let $A = (p \wedge q)$ and $B = (\sim p \vee r)$. The negation is $\sim(A \rightarrow B) \equiv A \wedge \sim B$. Substituting the values: $(p \wedge q) \wedge \sim(\sim p \vee r)$ Using De Morgan's Law,$\sim(\sim p \vee r) \equiv \sim(\sim p) \wedge \sim r \equiv p \wedge \sim r$. Therefore,the expression becomes: $(p \wedge q) \wedge (p \wedge \sim r)$ By the associative and idempotent laws,this simplifies to: $p \wedge q \wedge (\sim r)$.

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

Similar Questions

If $p$: It is raining and $q$: It is pleasant,then the symbolic form of "It is neither raining nor pleasant" is

Which of the following is the negation of the statement "For all $M > 0$,there exists $x \in S$ such that $x \geqslant M$"?

Which of the following quantified statements is true?

If the inverse of the conditional statement $p \to (\sim q \wedge \sim r)$ is false,then the respective truth values of the statements $p, q,$ and $r$ are:

If $p: \text{A man is happy}$,$q: \text{A man is rich}$,then the symbolic form of '$\text{A man is neither happy nor rich}$' is

Vedclass Test Series

Exam Paper Generator

Online Exam Module