(C) We test the expression $(p \wedge \sim q) \Rightarrow (p \vee q)$ using a truth table:$p, q$$p \wedge \sim q$$p \vee q$$(p \wedge \sim q) \Rightar

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(C) We test the expression $(p \wedge \sim q) \Rightarrow (p \vee q)$ using a truth table:$p, q$$p \wedge \sim q$$p \vee q$$(p \wedge \sim q) \Rightarrow (p \vee q)$$T, T$$F$$T$$T$$T, F$$T$$T$$T$$F, T$$F$$T$$T$$F, F$$F$$F$$T$Since all values in the final column are $T$,the expression is a tautology when $* = \wedge$ and $\square = \vee$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

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Let $, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

JEE MAIN 2021 All JEE MAIN

A
$* = \vee, \square = \vee$
B
$* = \wedge, \square = \wedge$
C
$* = \wedge, \square = \vee$
D
$* = \vee, \square = \wedge$

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Let $*, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p * \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

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Rewrite the following statement in the form "$p$ if and only if $q$":$p:$ If you watch television,then your mind is free and if your mind is free,then you watch television.

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Let $, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

Rewrite the following statement in the form "$p$ if and only if $q$":
$p:$ If you watch television,then your mind is free and if your mind is free,then you watch television.

For each of the following compound statements,first identify the connecting words and then break it into component statements.
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