∼p∨q∨∼p∧q is equivalent to

Correct answer: (B) ∼p. ~p∨q∨~p∧q≡~p∧~q∨~p∧q (By De morgan's Law) ≡∼p∧∼q∨q (By complement laws) ≡~p∧t (By Identity Laws) ≡~p

Q31 / 69 · NTA Abhyas (JEE Main) 2020 · Mathematics · Mathematical Reasoning

$\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to

A
$p$
Correct answer
B
$\sim p$
C
$q$
D
$\sim q$

Solution

$~ (p \lor q) \lor (~ p \land q) \equiv (~ p \land ~ q) \lor (~ p \land q)$ (By De morgan's Law)
$\equiv \sim p \land (\sim q \lor q)$ (By complement laws)
$\equiv ~ p \land t$ (By Identity Laws)

$\equiv ~ p$

Hence, the correct answer is option: 'B'.

∼p∨q∨∼p∧q is equivalent to

Solution

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$\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to