Q58 / 170 · Manipal (MET) 2017 · Mathematics

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

  • Correct answer
    A
    a contradiction
  • B
    a tautology
  • C
    either (a) or (b)
  • D
    neither (a) nor (b)

Solution

\(\begin{array}{ccccccc} \hline p & q & \sim p & \sim q & p \wedge \sim q & \sim p \vee q & \begin{array}{c} (p \wedge \sim q) \\ \wedge(\sim p \vee q) \end{array} \\ \hline \mathrm{T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} \\ \hline \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\ \hline \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} \\ \hline \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} \\ \hline \end{array}\) Clearly, \((p \wedge \sim q) \wedge(\sim p \vee q)\) is a contradiction.

Hence, the correct answer is option: 'A'.

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