Question

Identify the following sets as null set or singleton set.
(i) A = {x : x ∈N, 1 < x < 2}
(ii) B = The set of all even natural numbers which are not divisible by 2
(iii) C = {0}.
(iv) D = The set of all triangles having four sides.

Answer 1

Answer:

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Answer 2

Answer:

A: Null set

B: Null set

C: Singleton set

D: Null set

Step-by-step explanation:

To identify following sets as null set or singleton set.Let us first convert them into roaster form

(i) A = {x : x ∈N, 1 < x < 2}

=> In this set builder form ,as x belongs to natural number,and we know that 1,2,3,4... are natural numbers,so no natural number are lying between 1 and 2,thus set A is null set, A= {}

(ii) B = The set of all even natural numbers which are not divisible by 2

=> As we know that all even numbers are divisible by 2,hence all even natural numbers are also divisible by 2.Thus there is no such number which is even but not divisible by 2, so

Set B is also a null set, B={ }

(iii) C = {0}.

=> as we know that a set having a single element is known as a singleton set. Here set C is singleton set because it include only one element which is zero.

(iv) D = The set of all triangles having four sides.

=> as we know that a triangle is a closed figure composed of only three sides, so there are no such Triangles having four sides; thus set D don't have any element, hence set D is a null set .

Hope it helps you.