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

Which of the following statements is false when p is true and q is...

Which of the following statements is false when

p

is true and

q

is false?

Options

A $\left(p ⇒ q\right) ⇔ r$
B $\left(p ⇔ q\right) ⇒ r$
C $\left(q ⇒ r\right) ⇒ p$
D $\left(r ⇒ p\right) ⇒ q$

Correct answer

D. $\left(r ⇒ p\right) ⇒ q$

Step-by-step solution

$p$	$q$	$r$	\left(p ⇒ q\right) ⇔ r $</th> <th>\left(p ⇔ q\right) ⇒ r$	\left(q ⇒ r\right) ⇒ p $</th> <th>\left(r ⇒ p\right) ⇒ q$
T	F	T	F	T	T	F
T	F	F	T	T	T	F

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