Write the negation of the following statement:
$p:$ For every real number $x, x^{2} > x.$
$p:$ For every real number $x, x^{2} > x.$
(N/A) The negation of a statement involving the quantifier 'for every' is formed by replacing it with 'there exists' and negating the condition.
The negation of $p$ is:
$\sim p:$ There exists a real number $x$ such that $x^{2} \leq x.$
The negation of $p$ is:
$\sim p:$ There exists a real number $x$ such that $x^{2} \leq x.$
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If statements $p$ and $q$ are true and $r$ and $s$ are false,then the truth values of $\sim(p \rightarrow q) \leftrightarrow (p \wedge s)$ and $(\sim p \rightarrow q) \wedge (r \leftrightarrow s)$ are respectively:
Among the statements:
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$(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction
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DifficultJEE MAIN 2023
View SolutionStatement-$I$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a contradiction.
Statement-$II$: $(p$ $\rightarrow q) \Leftrightarrow (\sim q$ $\rightarrow \sim p)$ is a tautology.
Statement-$II$: $(p$ $\rightarrow q) \Leftrightarrow (\sim q$ $\rightarrow \sim p)$ is a tautology.
Difficult
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