Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then

($$\circ$$ denotes the composition of relations)

Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\} $$. Then domain A and range B are

A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$\cap$$ Q = $$\varphi $$ is

Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defined. Let g . f be injective mapping. Then