Recitation 15

To summarize the injectivity, surjectivity and bijectivity of the composition of two functions and its components, we have the following results.

Suppose f: A\to B, g: B\to C and h = g\circ f: A\to C.

  • If f and g are injective, then so is h.
  • If f and g are surjective, then so is h.
  • If h is injective, then so is f.
  • If h is surjective, then so is g.
  • It’s possible that h is injective but g is not.
  • It’s possible that h is surjective but f is not.

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