JEE 2023 Mathematics PYQ — The number of values of for which is a tautology, is:… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
The number of values of r∈{p,q,∼p,∼q} for which ((p∧q)⇒(r∨q))∧((p∧r)⇒q) is a tautology, is:
Choose the correct answer:
A.
3
B.
4
C.
1
D.
2
(Correct Answer)
Correct Answer:
2
Explanation
Expression: ((p∧q)⇒(r∨q))∧((p∧r)⇒q) Simplified: T∧(∼p∨∼r∨q) For Tautology, (∼p∨∼r∨q) must be T. - If r=q⇒∼p∨∼q∨q=T - If r=∼p⇒∼p∨p∨q=T Number of values of r=2
Explanation
Expression: ((p∧q)⇒(r∨q))∧((p∧r)⇒q) Simplified: T∧(∼p∨∼r∨q) For Tautology, (∼p∨∼r∨q) must be T. - If r=q⇒∼p∨∼q∨q=T - If r=∼p⇒∼p∨p∨q=T Number of values of r=2
