# Relations Examples

Here you will learn some relations examples for better understanding of relation concepts.

Example 1 : If A = {2, 4} and B = {3, 4, 5} then (A $$\cap$$ B) $$\times$$ (A $$\cup$$ B)

Solution : (A $$\cap$$ B) = {4} and (A $$\cup$$ B) = {2, 3, 4, 5}

$$\therefore$$ (A $$\cap$$ B) $$\times$$ (A $$\cup$$ B) = {(4, 2), (4, 3), (4, 4), (4, 5)}

Example 2 : If n(A) = 7 , n(B) = 8 and n(A $$\cap$$ B) = 4,then find-

(i)     n(A $$\cup$$ B)

(ii)     n(A $$\times B$$

(iii)     n((B $$\times$$ A)$$\times$$ A)

(iv)     n((A $$\times$$ B) $$\cap$$ (B $$\times$$ A))

(v)     n((A $$\times$$ B) $$\cup$$ (B $$\times$$ A))

Solution : (i)     11

(ii)     7 $$\times$$ 8 = 56

(iii)     56 $$\times$$ 7 = 392

(iv)     16

(v)     56 + 56 – 16 = 96

Example 3 : If N is a set of first 10 natural numbers and a relation R is defined as a + 2b = 10 where a, b $$\in$$ N. find inverse of R.

Solution : R = {(2, 4), (4, 3), (6, 2), (8, 1)}

$$R^{-1}$$ = {(4, 2), (3, 4), (2, 6), (1, 8)}

Practice these given relations examples to test your knowledge on concepts of relations.