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$$(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$$ is equivalent to $$(\sim p)$$ when $$r$$ is

JEE · Math · previous-year question

  1. A.$$p$$
  2. B.$$\sim p$$
  3. C.$$q$$correct
  4. D.$$\sim q$$

Answer

C. $$q$$

Explanation

The truth table .tg {border-collapse:collapse;border-spacing:0;} .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 $$ \wedge $$ q p $$ \wedge $$ $$ \sim $$ q p $$ \wedge $$ q $$ \Leftrightarrow $$ p $$ \wedge $$ $$ \sim $$ q T T F F T F F T F F T F T F F T T F F F T F F T T F F T Clearly p $$\wedge$$ q $$\Leftrightarrow$$ p $$\wedge$$ $$\sim$$ q $$\equiv$$ $$\sim$$ p $$\therefore$$ r = q

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