Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

Let p, q and r are three statements in which p is true. Consider...

Let p,qp, q and rr are three statements in which pp is true. Consider two compound statements
S1:(p⇒q)⇒r≡p⇒(q⇒r){S}_{1}: \left(p ⇒ q\right) ⇒ r ≡ p ⇒ \left(q ⇒ r\right)
S2:(p⟺q)⟺r≡p⟺(q⟺r){S}_{2}: \left(p ⟺ q\right) ⟺ r ≡ p ⟺ \left(q ⟺ r\right)
State in order, whether S1,S2{S}_{1}, {S}_{2} are true (T)& or false (F)

Options

  1. ATT
  2. BTF
  3. CFT
  4. DFF

Correct answer

C. FT

Step-by-step solution

pp qq rr \left(p ⇒ q\right) ⇒ r</th><th></th> <th>p ⇒ \left(q ⇒ r\right) \left(p ⟺ q\right) ⟺ r</th><th></th> <th>p ⟺ \left(q ⟺ r\right)
T T T T T T T
T F T T T F F
T T F F F F F
T F F T T T T
Practice Mathematical Reasoning on Quantrex Academy →

More from Mathematical Reasoning

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