Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

(p ˄ ~ q) ˄ ( ~ p ˅ q) is

1) A contradiction

2) A tautology

3) Either (a) or (b)

4) Neither (a) nor (b)

Solution: (1) A contradiction

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

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