Question

If n(A) = 5 and n(B) = 5, then find the number of possible bijections from A to B.​

Answer 1

Answer:

Step-by-step explanation:

A bijection from A to B is a function which maps every element of A to unique element of B i.e. injective.  

⟹n(B)≥n(A)

Also, it ensures that every element of B is an image of some element of A

⟹n(A)≥n(B)

∴n(A)=n(B)

⟹n(A)=  

2

m

​  

=n(B)

Let A={a  

1

​  

,a  

2

​  

,.....,a  

2

m

​  

 

​  

} and  

B={b  

1

​  

,b  

2

​  

,.....,b  

2

m

​  

 

​  

}

Let f:A→B defined by f(a  

i

​  

)=b  

i

​  

 is a bijection.

Any and all images of some fixed a  

i

​  

 appears in at least one such f. And each f is unique for each permutation (b  

1

​  

,b  

2

​  

,...b  

2

m

​  

 

​  

).

Hence, the num

Answer 2

Answer:

pls keep in a proper way

okk tq