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Which of the following is equivalent to the Boolean expression p $$\wedge$$ $$\sim$$ q ?

JEE · Math · previous-year question

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

Answer

D. $$\sim$$ (p $$\to$$ q)

Explanation

p q $$ \sim $$ p $$ \sim $$ q p $$ \to $$ q $$ \sim $$ (p $$ \to $$ q) q $$ \to $$ p $$ \sim $$ (q $$ \to $$ p) T T F F T F T F T F F T F T T F F T T F T F F T F F T T T F T F .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-baqh{text-align:center;vertical-align:top} p $$ \wedge $$ $$ \sim $$ q $$ \sim $$ p $$ \to $$ $$ \sim $$ q p $$ \to $$ $$ \sim $$ q $$ \sim $$ (p $$ \to $$ $$ \sim $$ q) F T F T T T T F F F T F F T T F p $$\wedge$$ $$\sim$$ q $$ \equiv $$ $$\sim$$ (p $$\to$$ q) Option (d)

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