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

The negation of ( p ∧ q) ∨ (p ∧ q) is

The negation of (p∧q)∨(p∧q)\left( p ∧ q\right) ∨ \left(p ∧ q\right) is$$

Options

  1. A(p∨q)∨(p∨q)\left(p ∨ q\right) ∨ \left( p ∨ q\right)
  2. B(p∨q)∧(p∨q)\left(p ∨ q\right) ∧ \left( p ∨ q\right)
  3. C(p∧q)∧(p∨q)\left(p ∧ q\right) ∧ \left( p ∨ q\right)
  4. D(p∧q)∧(p∨q)\left(p ∧ q\right) ∧ \left(p ∨ q\right)

Correct answer

B. (p∨q)∧(p∨q)\left(p ∨ q\right) ∧ \left( p ∨ q\right)

Step-by-step solution

Let, s:(p∧q)∨(p∧q)s: \left( p ∧ q\right) ∨ \left(p ∧ q\right)
s:((p∧q)∨(p∧q))s: \left( \left( p ∧ q\right) ∨ \left(p ∧ q\right)\right)
s:(p∧q)∧(p∧q)s: \left( p ∧ q\right) ∧ \left(p ∧ q\right)
$ s: \left(p ∨ q\right) ∧ \left( p ∨ q\right)
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