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Mathematics
Which of the following statements is a tautology ?
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Q. Which of the following statements is a tautology ?
JEE Main
JEE Main 2020
Mathematical Reasoning
A
$\sim\left(p\, \wedge\, \sim\, q\right) \rightarrow p\, \vee\, q$
B
$\sim\left(p\, \vee\, \sim\, q\right) \rightarrow\, p\, \wedge q$
C
$p \vee \left(\sim q\right) \rightarrow p \wedge q$
D
$\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q$
Solution:
$~\left(p \vee ~q\right) \to p \vee q$
$\left(~p \wedge q\right) \to p \vee q$
$~\left\{\left(~p \wedge q\right)\wedge \left(~p \wedge ~q\right)\right\}$
$~\left(~p \wedge ƒ\right)$