The negation of the statement (p wedge q) rig | vedclass

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

Question

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

Vedclass · Accepted Answer

$p \wedge q \wedge \sim r$

Vedclass · Answer

(C) To find the negation of the statement $(p \wedge q) \rightarrow (\sim p \vee r)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$.Let $A = (p \wedge q)$ and $B = (\sim p \vee r)$.Then,$\sim(A \rightarrow B) \equiv (p \wedge q) \wedge \sim(\sim p \vee r)$.Applying De Morgan's Law,$\sim(\sim p \vee r) \equiv \sim(\sim p) \wedge \sim r \equiv p \wedge \sim r$.So,the expression becomes $(p \wedge q) \wedge (p \wedge \sim r)$.By the Associative and Idempotent Laws,$(p \wedge q) \wedge p \wedge \sim r \equiv p \wedge q \wedge \sim r$.

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

Similar Questions

Which of the following statements is true?

Which of the following is not a statement?

If $p$ and $q$ are simple propositions,then $p \Leftrightarrow \sim q$ is true when

Simplify the following switching circuit and find the corresponding Boolean expression.

The negation of $(p \wedge (\sim q)) \vee (\sim p)$ is equivalent to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module