Sets, Relations and Functions - Arithmetic Aptitude Questions and Answers

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Let f : X → Y and g : Y → Z. Let h = g ◦ f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE?

If f is one-to-one then h is one-to-one and onto

If f is not onto then h is not onto

If f is not one-to-one then h is not one-to-one

If f is one-to-one then h is one-to-one

Answer : Option A

Explanation :

If f is one-to-one then h is one-to-one and onto

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