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MHT CET · Maths · Mathematical Reasoning

If the statement pattern \((p \wedge q) \rightarrow(r \vee \sim s)\) is false, then the truth values of p, q, r and s are respectively.

  1. A \(\mathrm{T}, \mathrm{F}, \mathrm{T}, \mathrm{F}\)
  2. B \(\mathrm{T}, \mathrm{T}, \mathrm{T}, \mathrm{F}\)
  3. C \(\mathrm{T}, \mathrm{T}, \mathrm{F}, \mathrm{F}\)
  4. D \(\mathrm{T}, \mathrm{T}, \mathrm{F}, \mathrm{T}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\mathrm{T}, \mathrm{T}, \mathrm{F}, \mathrm{T}\)

Step-by-step Solution

Detailed explanation

\((p \wedge q) \rightarrow(r \vee \sim s) \equiv \mathrm{F}\) \((p \wedge q) \equiv \mathrm{T}\) and \((r \vee \sim s) \equiv \mathrm{F}\)