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For a function `f:AtoB` such that `n(A)=a,n(B)=b(a,b in N)` then which of the following statements must be CORRECT?

A

if function is one - one, onto then `agtb`

B

if function is one - one into, then `agtb`

C

iif function si many - one, onto then `agtb`

D

if function is many - one into, then `altb`

Text Solution

Verified by Experts

The correct Answer is:
B, C
(A). If function is one-one & onto then `a=b` since every element of seb should have exactly one preimage in A. (B). For one-one, into function every element of set B should have either one pre-image or no preimage in set A `implies` no of elementsin set `Bge` no. of elements in A `becauseBgea`
(C) for many one onto function every element of set B should have one or more tha one pre-images in A.
`impliesn(B)len(A)impliesblea` or `ageb`
(D). for many- one into function `a in N` & `b in N`.
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