Question

If the set A has 5 elements and B has 4 elements then then how many relations are there
from B to A?
(a) 4
(b) 20
(C) 219
(d) 220​

Answer 1

Complete question:

If the set A has 5 elements and B has 4 elements then how many relations are there

from B to A?

(a) 4

(b) 20

(C) 2¹⁹

(d) 2²⁰

Answer:

The correct answer is option (d)2²⁰

Step-by-step explanation:

Given,

Set A has 5 elements and set B has 4 elements

To find,

The number of relations between B to A

Solution:

Recall the concepts

The cartesian product of two sets A and B is defined as

A XB = {(a,b): a ∈ A, b ∈ B}

The number of elements in the cartesian product AXB is

n(AXB) = n(A) ×n(B)

Every subset of the set AXB is a relation between A to B.

If n(AXB) =n, then the number of subsets of AXB = 2ⁿ

∴The number of relations between A to B =  2ⁿ

Here, it is given that the n(A) = 5 and n(B) = 4

Then the number of elements in the cartesian product B to A

n(BXA) = n(B) ×n(A)

= 4×5 = 20

n(BXA) = 20

The number of relations between B to A = the number of subsets of BXA = 2²⁰

Hence the correct answer is option (d)2²⁰

#SPJ3