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Question

Which are the empty sets ? Justify your answers

1) set of odd numbers that leave remainder zero,when divided by 2.

2)set of integers which lie between 2 and 3.


Solution

1) set of odd numbers that leave remainder zero,when divided by 2.
It is a empty set. 
Because the odd numbers divided by 2, the remainder is always 1. 
Here given is remainder is one, therefore in this no element is found. Therefore it is a null set. 

2)set of integers which lie between 2 and 3.
It is a empty set. 
​​​​​​Series of integer is given by
1,2,3,4,5,6...........
The adjacent number of 2 is 3. 2 and 3 are consecutive number of integer series. Which is clear in the above series. 
Therefore no element is found in set of integers which lie between 2 and 3. Therefore it is a empty set. 
 

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