let x = a b c and y = u v . which of the following arrow diagrams define functions from x to y
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Dr.Peterson
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Let's make it a little more readable:
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pka
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Do you understand the cross product of two sets is? That is [imath]X\times Y=\{(a,u),(a,v),(b,u).(b,v).(c,u).(c,v)\}[/imath]
The formal definition of a function [imath]f:X\to Y[/imath] is:
1) [imath]f\subseteq X\times Y[/imath]
2) Every element in [imath]X[/imath] is the first term of some pair in [imath]f[/imath]
3) No two terms of [imath]f[/imath] have the same first term.
Using those three requirements see which picture matches all three.
There is only one answer.
BTW: This is a faulty question because it should be [imath]Y=\{u,v,w\}[/imath]
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