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Mathematics
Let p, q, r be three statements. Then ∼ (p ∨ (q ∧ r)) is equal to
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Q. Let $p, q, r$ be three statements. Then $\sim (p \vee \left(q \wedge r\right))$ is equal to
KEAM
KEAM 2015
Mathematical Reasoning
A
$\left(\sim p \wedge \sim q\right)\wedge\left(\sim p \wedge \sim r\right)$
B
$\left(\sim p \vee \sim q\right) \wedge \left(\sim p \vee \sim r\right)$
C
$\left(\sim p \Lambda \sim q\right) \vee \left(\sim p \Lambda \sim r\right)$
D
$\left(\sim p \vee \sim q\right) \vee \left(\sim p \Lambda \sim r\right)$
E
$\left(\sim p \wedge \sim q\right)\vee \left(\sim p \vee\sim r\right)$
Solution:
$ \sim (p \vee(q \wedge r))=\sim p \wedge \sim(q \wedge r)$
$=\sim p \wedge(\sim q \vee \sim r) $
$=(\sim p \wedge \sim q) \vee(\sim p \wedge \sim r) $