Given any two functions f: A --> B, g: C --> D, define a new function h: AxC ---> BxD by h(x,y) (f(x)), g(y))(adsbygoogle = window.adsbygoogle || []).push({});

Show by counterexamples that the converse of each statement is false. What additional assumptions are needed to make the converses true?

(a) if both f and g are 1-1, then h is 1-1

(so show that if h is 1-1, both f and g are be 1-1)

(b) if both f and g are onto, then h is onto

(so show that if h is onto, then both f and g are onto)

i am having some trouble finding counterexamples,

for example can h(x) = x^2 - y^2, or does it have to be h(x,y) = (x^2, y^2)????

i believe the assumptions needed to make the converses true has to do with the domains of f and g.

but i'm pretty lost on this problem. any help is appreciated, thanks guys

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# Homework Help: Functions: 1-1, onto

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