Question 10517 – Set-Theory
April 20, 2024Question 9663 – Normalization
April 20, 2024Question 11067 – Set-Theory
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a ∈ A. Which of the following statements is always true for all such functions f and g?
Correct Answer: C
Question 10 Explanation:
g(f(a)) is a composition function which is A→B→C.
If h: A→C is a onto function, the composition must be onto, but the first function in the composition need to be onto.
So, B→C is must be onto.
If h: A→C is a onto function, the composition must be onto, but the first function in the composition need to be onto.
So, B→C is must be onto.
g is onto ⇒ h is onto
h is onto ⇒ f is onto
h is onto ⇒ g is onto
h is onto ⇒ f and g are onto
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