Let r $$\in$$ {p, q, $$\sim$$p, $$\sim$$q} be such that the logical statement r $$\vee$$ ($$\sim$$p) $$\Rightarrow$$ (p $$\wedge$$ q) $$\vee$$ r is a tautology. Then r is equal to :
JEE · Math · previous-year question
- A.p
- B.q
- C.$$\sim$$pcorrect
- D.$$\sim$$q
Answer
C. $$\sim$$p
Explanation
Clearly r must be equal to $$\sim$$ p $$\because$$ $$\sim$$ p $$\vee$$ $$\sim$$ p = $$\sim$$ p and (p $$\wedge$$ q) $$\vee$$ $$\sim$$ p = p $$\therefore$$ $$\sim$$ p $$\Rightarrow$$ p = tautology.
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