The function F is on .
it means the element of B has a distnict & unique preimage on A.
And given that set A is finete.
Where we know that A has finite no of elements. Which are the distinct preimage of B.
So we from the given condition we know that B is also finite.
Given that F is on to
It implies that there exist distinct & unique element bi which belongs to B
F is a function it means that every element of A has a image in B.
Which show |A|《 |B|......(.1)
But given that F is on to which means
from 1 & 2 we can say that
A is finite . So B is finte. (Proved)
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