# surjective

• Nov 15th 2009, 11:35 AM
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
• Nov 15th 2009, 12:10 PM
Plato
Quote:

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.
• Nov 15th 2009, 02:38 PM
emakarov
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".