0

I came across a question which says- "If a set A contains 7 elements and the set B contains 8 elements, then number of one to one mappings from A to B is:"

The answer is given zero

The explanation for the answer says that since n(A) is not equal to n(B) where n is the cardinal numbers of set A and B, hence number of none one mappings is zero

But I don't think this should be the answer as it is not mentioned anywhere in the definition of one one function that its range must be equal to the co-domain...

Synthia
  • 3

1 Answers1

0

The answer given is wrong. As @Sisanta Chhatoi pointed out, the question was likely referring to the number of onto functions from A to B which would be $0$.

The correct answer would be $ ^{8}C_{7} \times 7! $, as you are picking 7 out of 8 elements from B, and permuting the 7 elements of A into those 7 elements of B.

Little trick: If you want to find the number of one one functions from A to B, then the condition $n(A) \leq n(B)$ has to be satisfied, and the number of such one - one functions is $^nP_r$ or $ ^nC_r \times r!$, where $n$ is $n(B)$ and $r$ is $n(A)$.

Hope this helped.

Bongo Man
  • 320