Relations Examples

RELATIONS EXAMPLES

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)}


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