Write the negation of the following statement:
$s:$ There exists a number $x$ such that $0 < x < 1.$
$s:$ There exists a number $x$ such that $0 < x < 1.$
- AThere exists a number $x$ such that $x \le 0$ or $x \ge 1.$
- BFor all numbers $x$,$0 < x < 1.$
- CThere does not exist a number $x$ such that $0 < x < 1.$
- DFor all numbers $x$,$x \le 0$ or $x \ge 1.$
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State the converse and contrapositive of the following statement:
$r:$ If it is hot outside,then you feel thirsty.
$r:$ If it is hot outside,then you feel thirsty.
Easy
View SolutionThe negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow ((\sim p) \vee q)$ is logically equivalent to
The statement $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to
Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.
The contrapositive of $\sim q \to p$ is equivalent to
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