Question

Which of the following sets are empty sets? Justify your answer.
(i) A = {x : x² = 4 and 3x = 9}.
(ii) The set of all triangles in a plane having the sum of their three angles less than 180.

Answer 1

From the destination of empty set

A set to be called empty if it will have zero elements.

i) A = {x : x² = 4 and 3x = 9}.

So, A is {2}

So,A is having one element.

Hence,A is non-empty set.

ii) The set of all triangles in a plane having the sum of their three angles less than 180.

Generally for a triangle,

 sum of three angle is always 180 degree.

So, no triangle,means zero elements in this set

Hence,empty set.

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Answer 2

Answer:

B = { x ∶ x ∈ N and x2= x} is not an empty set, because there is only one natural number whose square is equal to the number is self i.e. 1 or B = {1}.Read more on Sarthaks.com - https://www.sarthaks.com/1037751/which-of-the-following-are-empty-sets-justify-b-x-x-n-and-x-2-x

Step-by-step explanation:

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