If $$P, Q, R$$ are subsets of the universal set $$U$$, then
$$\left( {P \cap Q \cap R} \right) \cup \left( {{P^c} \cap Q \cap R} \right) \cup {Q^c} \cup {R^c}$$ is

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?

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