If A= x z⁺: x < 10 . and x is a multiple of 3 or 4 , where z⁺ is the set of positive integers, then the total number of symmetric relations on A is

Step-by-step solution

A relation on a set A is said to be symmetric iff (a, b) A (b, a) A, a, b A Here A= 3,4,6,8,9 Number of order pairs of A A=5 5=25 Divide 25 order pairs of A A in 3 parts as follows : aligned & Part -A:(3,3),(4,4),(6,6),(8,8),(9,9) & Part -B:(3,4),(3,6),(3,8),(3,9),(4,6), & (4,8),(4,9),(6,8),(6,9),(8,9) & Part-C:(4,3),(6,3),(8,3),(9,3),(6,4),(8,4), & (9,4),(8,6),(9,6),(9,8) aligned In part -A , both components of each order pair are same. In part -B , both components are different but not two such order pairs are pr