Let A 1 2 3 and B a b c aHow many 1 1 functions are there

Let A = {1, 2, 3} and B = {a, b, c}. (a)How many 1 – 1 functions are there from A to B? Explain. List all of them Example, one of them is f(a) = c f(b) = b f(c) = a

Solution

In 1-1 functions no distinct elements in domain map to the same element in codomain

So, 1 can be mapped in 3 ways

2 can be mapped to remaining 2 elements and

3 to the last remaining elements

So, 3*2=6 functions

6 functions are:

f(1)=a,f(2)=b,f(c)=c

f(1)=a,f(2)=c,f(c)=b

f(1)=b,f(2)=c,f(c)=a

f(1)=b,f(2)=a,f(c)=c

f(1)=c,f(2)=a,f(c)=b

f(1)=c,f(2)=b,f(c)=a