Sets

If I am not mistaken this question is from KVPY 2012.

The number of tuples (a,b) is n²(since there are n ways to chose a and n ways to chose b).

Out of these n² pairs B must contain n of these pairs of the form(x,x).

We are left with n(n-1) pairs.For each pair,there are 2 options-B may or may not have that pair.

Hence the number of good subsets=

2\times 2\times 2\times \cdots = 2^{n(n-1)}