Q17 of 109 Page 1

State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

Given set {1,2,3} and relation R = {(1, 2), (2, 1)}.

For relation R to be transitive:

R={(1,2),(2,3),(1,3)}

But in the given relation:

⇒ (2,3) and (1,3) ∉ R

Hence, Given Relation R is not transitive.

A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x,y) : y is one half of x; x, y ϵA} is a relation on A, then write R as a set of ordered pairs.

Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b iff “a is a divisor of b.” Write R as a set of ordered pairs.

Let R = {(a, a³) : a is a prime number less than 5} be a relation. Find the range of R.

Show that R is an equivalence relation on the set Z of integers given by R = {(a, b) : 2 divides a – b}. Write the equivalence class [0].