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Mathematical Reasoning
hard
Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is
A
$\sqrt{5}$ is an integer or $5$ is irrational is
B
$\sqrt{5}$ is not an integer and $5$ is not irrational
C
$\sqrt{5}$ is an integer and $5$ is irrational
D
$\sqrt{5}$ is not an integer or $5$ is not irrational
(JEE MAIN-2020)
Solution
$\mathrm{p}=\sqrt{5}$ is an integer.
$\mathrm{q}: 5$ is irrational
$\sim(p \vee q) \equiv \sim p \wedge \sim q$
$\sqrt{5}$ is not an integer and $5$ is not irrational
Standard 11
Mathematics