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  3. 5. let x, y and z be sets. let f : x ! y and...

5. Let X, Y and Z be sets. Let f : X ! Y and...

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Advance Math

5. Let X, Y and Z be sets. Let f : X ! Y and g : Y ! Zfunctions.
(a) (3 Pts.) Show that if g f is an injective function, then fis an injective function.
(b) (2 Pts.) Find examples of sets X, Y and Z and functions f: X ! Y and g : Y ! Z such that g f is
injective but g is not injective.
(c) (3 Pts.) Show that if g f is a surjective function, then gis a surjective function.
(d) (2 Pts.) Find examples of sets X, Y and Z and functions f: X ! Y and g : Y ! Z such that g f is
surjective but f is not injective.

Answer & Explanation Solved by verified expert
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For part d of the question I know it has asked for mappings fand g such that got is    See Answer
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