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The statement $$\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)$$ is

JEE · Math · previous-year question

  1. A.a tautologycorrect
  2. B.equivalent to $$\left( { \sim p} \right) \vee \left( { \sim q} \right)$$
  3. C.a contradiction
  4. D.$$p \vee q$$

Answer

A. a tautology

Explanation

Making truth table (Let $(p \wedge \sim q) \Rightarrow(p \Rightarrow \sim q)=E$ ) .tg {border-collapse:collapse;border-spacing:0;width:100%} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} $p$ $q$ $\sim p$ $\sim q$ $p \wedge \sim q$ $p \Rightarrow \sim q$ $E$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\mathrm{F}$ $\mathrm{T}$ $\mathrm{T}$ $\therefore E$ is a tautology

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