UGC-NET Computer Science Discrete Mathematics Questions with Explanation

In this Blog we are providing all the UGC-NET Computer Science previous year Questions with explanation:

Q : 1 Consider a set A = {1, 2, 3, …….., 1000}. How many members of A shall be divisible by
3 or by 5 or by both 3 and 5 ?

(UGC-NET Computer Science December 2014 Paper 2)

(A) 533
(B) 599
(C) 467
(D) 66

Answer: (C)

Explanation:

Given Set is A = {1, 2, 3, …….., 1000}.
The members of 'A' which are divisible by 3 are given by {3,6,9,12...,999} these are total 333 elements.
The members of 'A' which are divisible by 5 are given by {5,10,15,20,...,1000} these are total 200 elements.
The members of 'A' which are divisible by both 3 and 5 i.e. divisible by 15 are given by {15,30,45,...,990} these are total 66 elements.

So, we have to find How many members of A shall be divisible by
3 or by 5 or by both 3 and 5?
i.e. No. of elements divisible by 3 +  No. of elements divisible by 5 -  No. of elements divisible by 15. 
(Union operation n(X union Y)=n(X)+n(Y) - n(X intersection Y))

=> 333 + 200 - 66=533 - 66 = 467.

This question was taken from UGC-NET Computer Science December 2014 Paper 2.