Skip to content
dronacharya.ai
← JEE Main 2022 · 24 Jun · Shift 1
MathematicsSingle correct+4 / -1Question 20 of 90

JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 20

The number of choices for Δ∈{∧,∨,⇒,⇔}\Delta\in\{\wedge,\vee,\Rightarrow,\Leftrightarrow\}, such that (p Δ q)⇒((p Δ∼q)∨((∼p) Δ q))(p\,\Delta\,q)\Rightarrow\left((p\,\Delta\sim q)\vee((\sim p)\,\Delta\,q)\right) is a tautology, is :

Choose one option
Answer and worked solution

Official answer: B

Test each connective.

  • ∧\wedge: with p=q=p=q= T the premise holds but (p∧∼q)∨(∼p∧q)(p\wedge\sim q)\vee(\sim p\wedge q) is false. Not a tautology.
  • ∨\vee: the conclusion (p∨∼q)∨(∼p∨q)(p\vee\sim q)\vee(\sim p\vee q) is always true. Tautology.
  • ⇒\Rightarrow: the conclusion (∼p∨∼q)∨(p∨q)(\sim p\vee\sim q)\vee(p\vee q) is always true. Tautology.
  • ⇔\Leftrightarrow: with p=qp=q the premise holds but both p⇔∼qp\Leftrightarrow\sim q and ∼p⇔q\sim p\Leftrightarrow q are false. Not a tautology.

So 2 choices.

(B)

Topics:Mathematical reasoning
← Previous questionNext question →