Condition for a function to be injective

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dpa
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Homework Statement


Do all the preimages on X need to have a (and of course I know only one but) image in Y for the f:x->y to be injective?
IS THE FOLLOWING FUNCTION INJECTIVE SINCE ONE ELEMENT OF FIRST DOES NOT HAVE ANY IMAGE
Arrow diagram of a function f from the left set to the right set: three left elements each map by a line to a distinct right element, and one left element has no arrow leaving it.


Homework Equations





The Attempt at a Solution


Thank You.
 
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  • Arrow diagram of a function f from a left set to a right set: three left-hand points each map by a line to a distinct right-hand point, and one left-hand point has no arrow.
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The way you have shown it, f is not a function from X to Y.