The Boolean expression (p wedge sim q) vee q | vedclass

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

Question

(A) Let the expression be $E = (p \wedge \sim q) \vee q \vee (\sim p \wedge q)$.Using the distributive law,$(p \wedge \sim q) \vee q \equiv (p \vee q)

Vedclass · Accepted Answer

$p \vee q$

Vedclass · Answer

(A) Let the expression be $E = (p \wedge \sim q) \vee q \vee (\sim p \wedge q)$.Using the distributive law,$(p \wedge \sim q) \vee q \equiv (p \vee q) \wedge (\sim q \vee q)$.Since $(\sim q \vee q) \equiv T$ (Tautology),we have $(p \vee q) \wedge T \equiv p \vee q$.Now,substitute this back into the expression:$E \equiv (p \vee q) \vee (\sim p \wedge q)$.Using the distributive law again,$(p \vee q) \vee (\sim p \wedge q) \equiv (p \vee q \vee \sim p) \wedge (p \vee q \vee q)$.Since $(p \vee \sim p) \equiv T$,we have $(T \vee q) \wedge (p \vee q)$.Since $(T \vee q) \equiv T$,we have $T \wedge (p \vee q) \equiv p \vee q$.Thus,the expression is equivalent to $p \vee q$.

The Boolean expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to:

Similar Questions

$S_1$: If $-7$ is an integer,then $\sqrt{-7}$ is a complex number.
$S_2$: $-7$ is not an integer or $\sqrt{-7}$ is a complex number.

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

Let $S$ be a non-empty subset of $R$. Consider the statement $p : x \in S$ is a rational number such that $x > 0$. Which of the following is the negation of $p$?

The negation of the converse of the statement $p \lor q$ is:

If $\sim p \lor q$ is false, then which of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module