Question

Which of the following are empty sets? Justify your answer.(i) Set of integers which lie between 2 and 3.(ii) Set of natural numbers that are less than 1.(iii) Set of odd numbers that have remainder zero, when divided by 2.

Answer 1

From the definition of empty set ,

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

i) Set of integers which lie between 2 and 3

1,2,3,4,5,......... are integers

between 2 and 3 no integers.

Hence empty set

ii) Set of natural numbers that are less than 1.

1,2,3,4,5,......... are natural numbers.

No, natural number is less than one

Hence,empty set.

iii) Set of odd numbers that have remainder zero, when divided by 2.

1,3,5,7,9......... are odd numbers

when divided by 2 we will not get reminder 0.Always we will get reminder 1.

Hence,empty set.

Answer 2

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