(C) Step $1$: Use the logical equivalence $A \to B \equiv \sim A \vee B$.Step $2$: Apply this to the given expression: $(p \vee q) \to \sim r \equiv \

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$(\sim p \wedge \sim q) \vee \sim r$

(C) Step $1$: Use the logical equivalence $A \to B \equiv \sim A \vee B$.Step $2$: Apply this to the given expression: $(p \vee q) \to \sim r \equiv \sim (p \vee q) \vee \sim r$.Step $3$: Apply De Morgan's Law, which states $\sim (p \vee q) \equiv \sim p \wedge \sim q$.Step $4$: Substitute this back into the expression to get $(\sim p \wedge \sim q) \vee \sim r$.

Class 11 Mathematics Mathematical Reasoning Mathematical logic

Medium

The statement pattern $(p \vee q) \to \sim r$ is logically equivalent to

MHT CET 2026 All MHT CET

A
$(\sim p \vee \sim q) \vee \sim r$
B
$(\sim p \wedge \sim q) \wedge \sim r$
C
$(\sim p \wedge \sim q) \vee \sim r$
D
$(\sim p \vee \sim q) \wedge \sim r$

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The statement pattern $(p \vee q) \to \sim r$ is logically equivalent to

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For each of the following compound statements,first identify the connecting words and then break it into component statements.
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