Which of the following logical equivalences is true?
- A$p$ $\Rightarrow q \equiv \sim p$ $\Rightarrow \sim q$
- B$\sim (p \Rightarrow \sim q) \equiv \sim p \wedge q$
- C$\sim (\sim p \Rightarrow \sim q) \equiv \sim p \wedge q$
- D$\sim (p \Leftrightarrow q) \equiv [\sim (p$ $\Rightarrow q) \wedge \sim (q$ $\Rightarrow p)]$
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Similar Questions
$S_1$: If $-7$ is an integer,then $\sqrt{-7}$ is a complex number.
$S_2$: $-7$ is not an integer or $\sqrt{-7}$ is a complex number.
$S_2$: $-7$ is not an integer or $\sqrt{-7}$ is a complex number.
The negation of the statement pattern $\sim s \vee (\sim r \wedge s)$ is equivalent to
Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.
If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :
DifficultMHT CET 2026
View SolutionWrite the negation of the following statement:
Chennai is the capital of Tamil Nadu.
Chennai is the capital of Tamil Nadu.
Easy
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