The negation of the statement "The number is an odd number if and only if it is divisible by $3$."
- AThe number is an odd number but not divisible by $3$ or the number is divisible by $3$ but not odd.
- BThe number is not an odd number iff it is not divisible by $3$.
- CThe number is not an odd number but it is divisible by $3$.
- DThe number is not an odd number or is not divisible by $3$ but the number is divisible by $3$ or odd.
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Similar Questions
The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
DifficultMHT CET 2026
View SolutionCheck whether the following sentence is a statement. Give reasons for your answer.
"Every set is a finite set."
"Every set is a finite set."
Easy
View SolutionConsider the following statements:
$p: 2$ is an even prime number.
$q: \text{If } z_1 = 2 - i, z_2 = -2 + i \text{ where } i = \sqrt{-1}, \text{ then } \operatorname{Im}\left[\frac{1}{z_1 \bar{z}_2}\right] = -\frac{1}{5}$.
$r: \tan(-945^{\circ}) = -1$.
Which of the following has a truth value of True?
$p: 2$ is an even prime number.
$q: \text{If } z_1 = 2 - i, z_2 = -2 + i \text{ where } i = \sqrt{-1}, \text{ then } \operatorname{Im}\left[\frac{1}{z_1 \bar{z}_2}\right] = -\frac{1}{5}$.
$r: \tan(-945^{\circ}) = -1$.
Which of the following has a truth value of True?
Write the contrapositive and converse of the following statement:
$x$ is an even number implies that $x$ is divisible by $4.$
$x$ is an even number implies that $x$ is divisible by $4.$
Easy
View SolutionNegation of the statement "The payment will be made if and only if the work is finished in time." is
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