Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $$S$$ are

What is the maximum number of different Boolean functions involving $$n$$ Boolean variables?

The set $$\left\{ {1,\,\,2,\,\,3,\,\,5,\,\,7,\,\,8,\,\,9} \right\}$$ under multiplication modulo 10 is not a group. Given below are four plausible reasons.

Which one of them is false?

A relation $$R$$ is defined on ordered pairs of integers as follows: $$\left( {x,y} \right)R\left( {u,v} \right)\,if\,x < u$$ and $$y > v$$. Then $$R$$ is