Assignment:
Let f: X--->Y and g: Y--->Z be functions.
i. If both f and g are injective prove that g o f is injective.
ii. If both f and g are surjective prove that g o f is surjective
iii. If both f and g are bijective prove that g o f is bijective
iv. If g o f is bijection, prove that f is an injection and g is a surjection.
Provide complete and step by step solution for the question and show calculations and use formulas.