Q6 of 109 Page 1

If R is a symmetric relation on a set A, then write a relation between R and R^–1.

The relation between R and R^–1 on a Set A is as under:

⇒ R^-1 = {(b,a):(a,b)∈ R}

⇒ Clearly (a,b) ∈ R

⇒ (b,a) ∈ R^-1

i.e Domain(R)=Range(R^-1)

and Domain(R^-1)=Range(R)

Write the smallest reflexive relation of set A = {1, 2, 3, 4}.

If R = {(x,y) : x + 2y = 8} is a relation on N, then write the range of R.

Let R = {(x,y): |x² – y²| < 1} be a relation on set A = {1, 2, 3, 4, 5}. Write R as a set of ordered pairs.

If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x,y) : x ϵ A, y ϵB and x < y} is a relation from A to B, then write R^–1.

If R is a symmetric relation on a set A, then write a relation between R and R–1.