Question

Let A = { x , y , z} and B = {1, 2}. Find the number of relations from A to B.

Answer 1

It is given that A={ x,y,z } and B={ 1,2 } .

The formula to form a relation is A×B={ ( x,y ):x∈A,y∈B } .

So the relation of the given sets is,

{ ( x,1 ),( x,2 ),( y,1 ),( y,2 ),( z,1 ),( z,2 ) }

The formula to calculate the number of relation is,

2 na×nb

Here, n a is the number of elements in set A and n b is the number of elements in set B.

The number of relation is,

2 3×2 = 2 6 =64

Thus, the number of relations from A to B is 64.