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How many relations are possible from a set A of 'm' elements to another set B of 'n' elements?
Ans: A relation R from a set A to other set B is specified as any subset of A x B. If |A| = m and |B| = n, after that |A x B| =mn and thus number of possible subsets of A x B = 2mn. Every subset is a relation from A to B. So there are 2mn dissimilar types of relations from A to B.
1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o
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