Question

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

Answer 1

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

.

Now,

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

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

{ Φ, {(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, a), (b, b)}}

n(A) = 2 ⇒ n(A, A) = 2 × 2 = 4

Total number of relations = 2⁴ = 16

Answer 2

Answer:

Step-by-step explanation:

total no of relations = 2*2*2*2=16