If p and q are statements, then $\qquad$ is a contingency.

If p and q are statements, then $\qquad$ is a contingency.
  1. $\mathrm{p} \wedge \sim \mathrm{p}$
  2. $\mathrm{p} \vee \sim \mathrm{p}$
  3. $\mathrm{p} \vee \mathrm{q}$
  4. $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q})) \rightarrow \mathrm{q}$

Solution

Step 1 Identify the definitions: A contradiction is always false, a tautology is always true, and a contingency can be either true or false. Step 2 Evaluate option (A): \(p \wedge \sim p\) is always false (contradiction). Step 3 Evaluate option (B): \(p \vee \sim p\) is always true (tautology). Step 4 Evaluate option (C): \(p \vee q\) can be true or false depending on the values of \(p\) and \(q\), making it a contingency. Final Answer: C) \(p \vee q\)

Asked in: MHT CET 2024 (03 May Shift 1)

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