Which of the following statement pattern is contradiction?

Which of the following statement pattern is contradiction?
  1. $S_3 \equiv(\sim p \wedge q) \wedge(\sim q)$
  2. $S_2 \equiv(p \rightarrow q) \vee(p \wedge \sim q)$
  3. $S_1 \equiv(\sim p \vee \sim q) \vee(p \vee \sim q)$
  4. $S_4 \equiv(\sim p \wedge q) \vee(\sim q)$

Solution

$\begin{aligned} & S_3 \equiv(\sim p \wedge q) \wedge(\sim q) \\ & \equiv \sim p \wedge(q \wedge \sim q) \\ & \text { [Associative law] } \\ & \equiv \sim p \wedge c \\ & {[\because q \wedge \sim q \equiv c]} \\ & \equiv c \\ & {[\because p \wedge c \equiv c]} \\ & \end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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