Question

If the number of elements in a set A is 4 and that in set B is 5, then how many relations from set A to set B are possible?
1. 20
2. 9
3. 2²⁰
4. None of these.

Answer 1

Correct Answer - Option 3 : 2²⁰

Concept:

Set Theory:

• 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 and the number of subsets of (A × B) will be 2^pq.

 

Calculation:

It is given that n(A) = p = 4 and n(B) = q = 5.

The required number of relations from A to B = 2^4×5 = 2²⁰.