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Let f be a function from S to T and g be a function from T...

Let f be a function from S to T and g be a function from T to U.

Show the following:

  1. If f and g are injective, then their composition from S to U is injective
  2. If f and g are surjective, then their composition  from S to U is surjective
  3. If f and g are bijective, then their composition  from S to U is bijective
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