Assignment:
Qa. Prove by induction that (1^3+2^3+...+n^3)= [(1/2)n(n+1)]^2 for all n elements of N
Qb. Give an example of two functions f,g on Reals to Reals such that f does not equal g but such that f o g = g o f.
Qc. Show that if a,b elements of Real numbers then
i. max{a,b} = 1/2(a + b + abs(a-b)) and min{a,b}= 1/2(a+b-abs(a-b))
ii. min {a,b,c}= min{min{a,b},c}
Qd. Prove using math induction that if the sets S has n elements, then the power set of S, P(S), has 2^n elements.
Provide complete and step by step solution for the question and show calculations and use formulas.