Question

If the number of bijective functions from a set A to set B is 120,the n(A)+n(B) is equal to

Answer 1

Bijective function is both a one-to-one or injective function, and an onto or surjective function. This means that for every function f: A \(\rightarrow\) B, each member a of domain A maps to precisely one unique member b of codomain B.

There are certain features that make a bijective function:

• There is an equal number of members in the domain and codomain sets of a bijective function.
• A bijective graph meets any horizontal or vertical line drawn across it only once - no more, no less.
• In a bijective function, the cardinality of the sets are maintained. 
• The range of a bijective function f: A→B is the same as its codomain because the function gives the same results as the image of the codomain.
• In a bijective function f: A → B, each element of set A should be paired with just one component of set B and no more than that, and vice versa.

For fⁿ to be bijective , n(A) = n(B) = n and no. of fⁿ are = n! n! = 120

  ∴  n = 5  ∴  n(A) + n(B) = 10