a) Suppose g then f is "b) a Supnose

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Chapter2: Second-order Linear Odes
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(a) Suppose g: X → Y and f: Y → Z are functions. If f o g: X → Z is surjective,
then f is surjective.
(b) Suppose g: X → Y and f: Y → Z are functions. if f o g: X → Z is injective,
then f is injective.
Transcribed Image Text:(a) Suppose g: X → Y and f: Y → Z are functions. If f o g: X → Z is surjective, then f is surjective. (b) Suppose g: X → Y and f: Y → Z are functions. if f o g: X → Z is injective, then f is injective.
4. Prove or give a counterexample for each of the following statements. If you are giving
a counterexample, you must specify what X, Y, Z, f, and g are.
Transcribed Image Text:4. Prove or give a counterexample for each of the following statements. If you are giving a counterexample, you must specify what X, Y, Z, f, and g are.
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