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Let f : A → B and g : B → C denote two functions. Consider the following three statements:

  • S1 : If both f and g are injections then the composition function  : A → C is an injection.
  • S2 : If the function  : A → C is surjection and g is an injection then the function f is a surjection.
  • S3 : If h(a) = g(f(a)) and h(a) is onto then g must be onto, where ∀a, a ∈ A.

Which of the above statements is/are valid?

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Let f : A → B and g : B → 

S1: if f and g are injection fuction then composition function  gof :A → C is an injection. ----> this statement true its well known property.

S2:If the function gof : A → C is surjection and g is an injection then the function f is a surjection.

here keypoint is g is injection fuction.

means that  g(f(x) = g(y) -----> f(x) = y  so that fuction f is surjection

S3:If h(a) = g(f(a)) and h(a) is onto then g must be onto, where ∀aa ∈ A

all of the statement true. its all property .

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