Question

answer this question with reason?​

Answer 1

Answer:

{x ∈ Q : x² = 2 } is an empty set

Step-by-step explanation:

Concept used:

A set having no elements in it is called an empty set.

Given:

{x ∈ Q : x² = 2 }

Here, Q is the set of all rational numbers

The equation $x^2=2$ has solution

$x=\sqrt2\:and\:x=-\sqrt2$

But the numbers $\sqrt2\:and\:-\sqrt2$ both are irrational.

⇒ $\sqrt2\:and\:-\sqrt2$ ∉ Q

Hence, the set {x ∈ Q : x² = 2 } will not contain any elements.

That is, {x ∈ Q : x² = 2 } is an empty set

Answer 2

Answer:

D  are the sets.

Step-by-step explanation:

Rational numbers (Q) are the numbers which can be represented in the form of p/q where q is not equal to 0. Now

in option B +/- (2)^1/2 seems the right rational number to satisfy but since it is irrational number it cannot be counted in the answer.

Option C cannot be taken as square of */- 1 is 1 itself.

Hence we are left with an empty set of rational numbers that is D.