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

1.	Let A = {a, b}. List all relations on A and find their number.
Answer» Here, the total number of relations that can be defined from the set A to the set B is the number of possible subsets of A × B. When n (A) = p and n (B) = q, then n (A × B) = pq. There, the total number of relations is 2^pq. Then, A × A = {(a, a), (a, b), (b, a), (b, b)} The 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 Thus, the total number of relations = 2⁴ = 16

Answer»

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

There, the total number of relations is 2^pq.

Then,

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

The 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

Thus, the total number of relations = 2⁴ = 16

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