Thread: surjective

Some surjective functions from A to B are not injective( Here A and B are variables representing two sets. The universe is the set of all functions from A to B)

What would the open sentence using quanitifiers for this statement be.

there exists 2 elements in A such that if there exists an element of A for all elements of B then 2 elements of B are equal and the corresponding elements in a are not equal

Originally Posted by leinadwerdna

Some surjective functions from A to B are not injective( Here A and B are variables representing two sets. The universe is the set of all functions from A to B)

What would the open sentence using quanitifiers for this statement be.

there exists 2 elements in A such that if there exists an element of A for all elements of B then 2 elements of B are equal and the corresponding elements in a are not equal

That sentence is nonsense.
Please check the source and edit it so it is exactly as you find it in the source.

Well, this phrase is an attempted answer, not the problem statement.

Your sentence starts with "there exists 2 elements in A", but "Some surjective functions" is talking about functions from A -> B, not elements of A.

The outline of the sentence is: There exist a function f such that f is surjective and f is not injective. Then you may need to expand the definitions of "surjective" and "injective".