Question

Let A = {2, 3} and B= {3, 5} 

(i) Find (A × B) and n(A × B). 

(ii) How many relations can be defined from A to B?

Answer 1

Given: A = {2, 3} and B= {3, 5}

(i) (A × B) = {(2, 3), (2, 5), (3, 3), (3, 5)} 

Therefore, n(A × B) = 4 

(ii) No. of relation from A to B is a subset of Cartesian product of (A × B). 

Here no. of elements in A = 2 and no. of elements in B = 2. 

So, (A × B) = 2 × 2 = 4 

So, the total number of relations can be defined from A to B is 

= 2⁴ = 16