Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The set of rationals $\mathbb{Q}$ is closed in the real line $\mathbb{R}$. Reason R : The closure of $\mathbb{Q}$ in $\mathbb{R}$ is $\mathbb{R}$. In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

$\mathbb{Q}$ is neither open nor closed in $\mathbb{R}$! Its interior is empty ($\text{Int}(\mathbb{Q}) = \emptyset$) and its closure is all of $\mathbb{R}$ ($\bar{\mathbb{Q}} = \mathbb{R}$).

Answer 1

The Correct Option is D