Let p be the statement " x is an irrational number", q be the statement " y is a transcendental number", and r be the statement " x is a rational number iff y is a transcendental number". Statement -1 : r is equivalent

Correct answer: D. Statement -1 is true, Statement -2 is false. Given statement r= p rightarrow q Statement -1: r_1=(p q) ( p q) Statement -2: r_2= (p rightarrow q)=(p q) ( q p) From the truth table of r, r_1 and r_2 , r=r_1 . Hence Statement -1 is true and Statement -2 is false.

JEE Main 2008

Exam: JEE Main
Year: 2008
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2008 · Mathematics · Mathematical Reasoning

Let p be the statement " x is an irrational number", q be the...

Let

p

be the statement "

x

is an irrational number",

q

be the statement "

y

is a transcendental number", and

r

be the statement "

\mathrm{x}

is a rational number iff

\mathrm{y}

is a transcendental number". Statement

-1

r

is equivalent to either

q

p

Statement

-2: r

is equivalent to

\sim(p \leftrightarrow \sim q)

Options

AStatement $-1$ is false, Statement $-2$ is true
BStatement $-1$ is true, Statement $-2$ is true, Statement $-2$ is a correct explanation for Statement $-1$
CStatement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$ .
DStatement $-1$ is true, Statement $-2$ is false.

Correct answer

D. Statement $-1$ is true, Statement $-2$ is false.

Step-by-step solution

Given statement

r=\sim p \leftrightarrow q

Statement

-1: r_1=(p \wedge \sim q) \vee(\sim p \wedge q)

Statement

-2: r_2=\sim(p \leftrightarrow \sim q)=(p \wedge q) \vee(\sim q \wedge \sim p)

From the truth table of

r, r_1

and

r_2

r=r_1

. Hence Statement

-1

is true and Statement

-2

is false.

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 JEE Main PYQs