If p and q are two logical statements, then (p ∨ q)→ (p → q) is equivalent to

Correct answer: B. p → (p ∨ q) ∵ S → t ≡ S ∨ t ∴ (p ∨ q) → (p → q) ≡ (p ∨ q) ∨ (p → q) ≡ (p ∨ q) ∨ ( p ∨ q) ≡ (p ∨ p) ∨ q ≡ t ∨ q ≡ t Also, p → (p ∨ q) ≡ p ∨ (p ∨ q) ≡ t

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If p and q are two logical statements, then (p ∨ q)→ (p → q) is...

p and q

are two logical statements, then \left(p ∨ q\right)\to \left(p \to q\right) is equivalent to

Options

A $p ∧ q$
B $p \to \left(p ∨ q\right)$
C $p ∨ q$
D $\left(p ∨ q\right) ↔ \left(p ∧ q\right)$

Correct answer

B. $p \to \left(p ∨ q\right)$

Step-by-step solution

∵ S \to t ≡ S ∨ t

∴ \left(p ∨ q\right) \to \left(p \to q\right) ≡ \left(p ∨ q\right) ∨ \left(p \to q\right)

≡ \left(p ∨ q\right) ∨ \left( p ∨ q\right)

≡ \left(p ∨ p\right) ∨ q

≡ t ∨ q ≡ t

Also,

p \to \left(p ∨ q\right) ≡ p ∨ \left(p ∨ q\right) ≡ t

Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

Negation of p ∧ (q ∧ ~ (p ∧ q)) is JEE Main 2023 The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to… JEE Main 2023 The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is JEE Main 2023 Among the two statements ( S _ 1 ): (p ⇒ q) ∧ (p ∧ (~ q)) is a contradiction and ( S _ 2… JEE Main 2023 The converse of ((~ p) ∧ q) ⇒ r is JEE Main 2023 The number of ordered triplets of the truth values of p, q and r such that the truth… JEE Main 2023 The statement ~ [p ∨ (~ (p ∧ q))] is equivalent to JEE Main 2023 The negation of the statement (p ∨ q) ∧ (q ∨ (~ r)) is JEE Main 2023 The negation of ( p ∧ ( - q ) ) ∨ ( - p ) is equivalent to JEE Main 2023 Negation of (p → q) → (q → p) is JEE Main 2023 Among the statements (S1): (p ⇒ q) ∨ ((~ p) ∧ q) is a tautology (S2): (q ⇒ p) ⇒ ((~ p) ∧… JEE Main 2023 Statement ( P ⇒ Q ) ∧ ( R ⇒ Q ) is logically equivalent to JEE Main 2023 Which of the following statements is a tautology? JEE Main 2023 The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to JEE Main 2023 The number of values of r ∈ \ p, q, ~ p, ~ q\ for which ((p ∧ q) ⇒ (r ∨ q) ∧ ( (p ∧ r) ⇒… JEE Main 2023 Consider: (S1): (p ⇒ q) ∨ (p ∧ (~ q)) is a tautology. (S2): ((~ p) ⇒ (~ q)) ∧ ((~ p) ∨ q)… JEE Main 2023 Full Mathematical Reasoning list Mathematical Reasoning JEE Maths PYQs JEE Mathematics PYQs All NTA Abhyas JEE Main PYQs