MHT CET · Maths · Mathematical Reasoning
If p and q are statements, then \(\qquad\) is a contingency.
- A \(\mathrm{p} \wedge \sim \mathrm{p}\)
- B \(\mathrm{p} \vee \sim \mathrm{p}\)
- C \(\mathrm{p} \vee \mathrm{q}\)
- D \((\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q})) \rightarrow \mathrm{q}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{p} \vee \mathrm{q}\)
Step-by-step Solution
Detailed explanation
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) \(p \vee q\)
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) \(p \vee q\)
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