Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20199 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2019 · 9 January · Evening Shift · Mathematics · Mathematical Reasoning

The logical statement [~ (~ p ∨ q) ∨ (p ∧ r)] ∧ (~ q ∧ r) is...

The logical statement [ ( p∨q)∨(p∧r)]∧( q∧r)isequivalentto\left[~ \left(~ p ∨ q\right) ∨ \left(p ∧ r\right)\right] ∧ \left(~ q ∧ r\right) is equivalent toThe logical statement [~ (~ p ∨ q) ∨ (p ∧ r)] ∧ (~ q ∧ r) is equivalent to

Options

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

Correct answer

B. (p∧r)∧ q\left(p ∧ r\right) ∧ ~ q

Step-by-step solution

\left[~ \left(~ p ∨ q\right) ∨\left(p ∧ r\right)\right] ∧ \left(~ q ∧ r\right)

= \left[\left(p ∧ ~ q\right) ∨ \left(p ∧ r\right)\right] ∧ \left(~ q ∧ r\right)</p><p>Bydistributivelaw</p><p></p><p>By distributive law</p><p>= p ∧ \left(~ q ∨ r\right)∧( q∧r)∧ \left(~ q ∧ r\right)
The logical statement [~ (~ p ∨ q) ∨ (p ∧ r)] ∧ (~ q ∧ r) is equivalent to

p∧( q∧r)≡(p∧r)∧ qp ∧ \left(~ q ∧ r\right) ≡ \left(p ∧ r\right) ∧ ~ q

=p∧∼q∧r= p ∧ ∼ q ∧ r

By Associative law

=(p∧r)∧ q= \left(p ∧ r\right) ∧ ~ q

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 JEE Main PYQs