Question

A= {1, 2, 3, 4, 5} ,B = {a,b,c.d} and f.A-B
is given by f= {( 1,d) (2,a) (3,c) (4.a) (5,c)}
Then f ({1, 2, 3}) = ?​

Answer 1

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 f

1

,f

2

,f

3

and f

4

are the functions from A to B.

f

1

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

f

2

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

f

3

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

f

4

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

We can verify that f

1

,f

2

,f

3

and f

4

are bijective from A to B.

Now,

f

1

−1

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

f

2

−1

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

f

3

−1

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

f

4

−1

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

Answer 2

Answer:

120a²c²{(1,d²),2(1,d²),3(1,d²)}

Step-by-step explanation:

f (1,2,3)

= {(1,d) (2,a) (3,c) (4,a) (5,c)} × (1,2,3)

=(120a²c²,120d²a²c²)×(1,2,3)

=120a²c²(1,d²)×(1,2,3)

=120a²c²(1,d²),240a²c²(1,d²),360a²c²(1,d²)

=120a²c²{(1,d²),2(1,d²),3(1,d²)}