Relations and Functions Test - 23

A relation R in a set A is called empty relation, if no element of A is related to any element of A.

i.e. R =  ϕ ⊂ (A x A). 

A relation R in a set A is called universal Relation if each element of A is related to every element of A. i.e, R = A x A

A function f : X → Y is invertible if and only if f is one - one & onto or bijective.

Onto function : 

A function  f : X → Y is known to be onto or surjective if every element of Y is the image of some element of X under f 

i.e. ∀y ∈ Y

there exists an element x in X 

such that  f(x) = y 

Given,

Let a set A = {1, 2, 3}

Then,

A x A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

Number of elements = 9 & no. of element in set A = 3.

Number of subsets = 3⁹

= 729

Thus, the number of binary operations are 729.