Question

Which of the following are empty sets ? why ?
(i) A = { a | a is a natural number smaller than zero.}
(ii) B = {x | x2 = 0}​

Answer 1

Answer:

B is the correct answer of this question

Answer 2

Answer:

Step-by-step explanation:

(i) By definition, we know that there is no natural number smaller than zero(Natural numbers are the positive integers that start from one and ends at infinity)

So, there is no element in the set $A$

⇒ $A$ is an empty set

⇒ $A = \phi$

(ii) We know that the square of a real number is always non-negative

So,

$\forall x \in \mathbb{R}: x \neq 0 \implies x^2 > 0\\\text{and } x^2 = 0 \text{ if and only if } x = 0$

⇒ B ={0}  (NOTE: Here the set B contains an element 0)

⇒ B is not an empty set