Let A = {a, b}. List all relations on A and find their number.

Asked by Aaryan | 1 year ago |  58

##### Solution :-

The total number of relations that can be defined from a set A to a set B is the number of possible subsets of A × B. If n (A) = p and n (B) = q, then n (A × B) = pq.

So, the total number of relations is 2pq.

Now,

A × A = {(a, a), (a, b), (b, a), (b, b)}

Total number of relations are all possible subsets of A × A:

[{(a, a), (a, b), (b, a), (b, b)}, {(a, a), (a, b)}, {(a, a), (b, a)},{(a, a), (b, b)}, {(a, b), (b, a)}, {(a, b), (b, b)}, {(b, a), (b, b)}, {(a, a), (a, b), (b, a)}, {(a, b), (b, a), (b, b)}, {(a, a), (b, a), (b, b)}, {(a, a), (a, b), (b, b)}, {(a, a), (a, b), (b, a), (b, b)}]

n (A) = 2 ⇒ n (A × A) = 2 × 2 = 4

∴ Total number of relations = 24 = 16

Answered by Sakshi | 1 year ago

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