JEE 2023 — Mathematics PYQJEE | Mathematics | 2023Which of the following statements is a tautology?Choose the correct answer:A. p∨(p∧q)B. (p∧(p→q))→∼qC. (p∧q)→(∼p→q)Correct Answer: (p∧q)→(∼p→q)ExplanationUsing the identity X→Y≡∼X∨Y: ≡∼(p∧q)∨(p∨q) ≡(∼p∨∼q)∨(p∨q) ≡(∼p∨p)∨(∼q∨q) ≡T∨T≡T Ap∨(p∧q)B(p∧(p→q))→∼qC(p∧q)→(∼p→q)Dp→(p∧(p→q))Show Answer SExplanationUsing the identity X→Y≡∼X∨Y: ≡∼(p∧q)∨(p∨q) ≡(∼p∨∼q)∨(p∨q) ≡(∼p∨p)∨(∼q∨q) ≡T∨T≡T
