Left( { ∼ left( {p vee q} right)} right) vee left( { ∼ p wedge q} right) is logically equi

English

Gujarati

Hindi

Mathematical Reasoning

normal

$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to

A

$ \sim p$

B

$p$

C

$q$

D

$ \sim q$

Solution

$ \sim (p \vee q) \vee ( \sim p \wedge q) \equiv ( \sim \;p \vee {\rm{ }} \sim \;q) \vee ( \sim \;p \wedge q)$

$ \sim p \wedge ( \sim q \vee q) \equiv {\rm{ }} \sim p \wedge t \equiv \sim p$

Standard 11

Mathematics

Share

Similar Questions

Consider the two statements :

$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology

$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.

Then :

medium

(JEE MAIN-2021)

Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

easy

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

medium

(JEE MAIN-2021)

If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively

hard

(JEE MAIN-2019)

Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

hard

(JEE MAIN-2017)