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.