Q20 of 76 Page 2

Let R be the relation on Z defined by R = {(a, b) Z, a – b is an integer}. Find the domain and range of R.

Given, R = {(a, b) Z, a – b is an integer}

Z denotes integer, and here a and b both are integers

We know that difference of two integers is always an integer

∴ a and b can be any integer in relation R

⇒ The domain of relation R = Z (as a Z)

The range of relation R = Z (as b Z)

Let A= {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by

R= {(a, b): a, b A, b is exactly divisible by a}

i. Write R in roster form

ii. Find the domain of R

iii. Find the range of R.

Figure 2.15 shows a relationship between the sets P and Q. Write this relation in

a. Set builder form

b. Roster form

c. What is its domain and range?

For the relation R₁ defined on R by the rule (a, b) R₁ 1 + ab > 0. Prove that: (a, b) R₁ and (b,c) R₁ (a, c) R₁ is not true for all a, b, c R.

Let R be a relation on N x N defined by (a, b) R (c, d) a + d = b + c for all (a, b), (c, d) N x N.

Show that:

i. (a, b) R (a, b) for all (a, b) N x N

ii. (a, b) R (c, d) (c, d) R (a, b) for all (a, b), (c, d) N x N

iii. (a, b) R (c, d) and (c, d) R (e, f) (a, b) R (e, f) for all (a, b), (c, d), (e, f) N × N