Question

A function f: A -> B where A= {a.b.c}, B = {1.2.3.4}. How many functon can be defined from A to B which are not one-one such that 2 ∈ f(A)

Answer 1

Answer:

A function f: A -> B where A= {a.b.c}, B = {1.2.3.4}. How many functon can be defined from A to B which are not one-one such that 2 ∈ f(A)

Answer 2

$\blue{\huge{\underline{\underline{Answer:-}}}}$

We know, A={1,2,3,4} and B={a,b,c,d}

⇒  We know that, a function from A to B is said to be bijection if it is one-one and onto.

⇒  This means different elements of A has different images in B. 

⇒  Also each element of B has pre-image in A.

Let f1,f2,f3 and f4 are the functions from A to B.

f1={(1,a),(2,b),(3,c),(4,d)}

f2={(1,b),(2,c),(3,d),(4,a)}

f3={(1,c),(2,d),(3,a),(4,b)}

f4={(1,d),(2,a),(3,b),(4,c)}

We can verify that f1,f2,f3 and f4 are bijective from A to B.

Now,

f1−1={(a,1),(b,2),(c,3),(d,4)}

f2−1={(b,1),(c,2),(d,3),(a,4)}

f3−1