Question

Let P = {1, 2, 3} and Q = {4, 5, 6, 7}. What is the number of distinct relations from Q to P?
1. 12
2. 2²⁵
3. 4094
4. 4096

Answer 1

Correct Answer - Option 4 : 4096

Concept:

Let A and B are two sets, having a number of elements n(A) and n(B) respectively.

Then, the number of distinct relation = \(\rm 2^{n(A)\times n(B)}\)

Calculation:

Here,  P = {1, 2, 3} and Q = {4, 5, 6, 7}

n(P) = 3

n(Q) = 4

∴ Number of distinct relation = \(\rm 2^{n(A)\times n(B)}\)

\(\rm 2^{n(P)\times n(Q)} \\=2^{3\times 4}\)

= 2¹²

= 4096

Hence, option (4) is correct.