Assume each function in the assertions below are from Z+ to R+. Prove that the proposition is true, using the definition of the asymptotic notation(s) or disprove it by giving a counter-example and explaining how the counter-example disproves the assertion.

Assume each function in the assertions below are from Z+ to R+. Prove that the propo- sition is true, using the definition of the asymptotic notation(s) or disprove it by giving a counter-example and explaining how the counter-example disproves the assertion (a) Proposition 1: If fi(n) E O(9i (n), f2(n) e O(92(n)) and gi(n) e O(g2(n)) then fi(n) f2(n) E O(92(n)). [15 points] (b) Proposition 2: fi (n) E 0(g(n)) and /2 (n) 0(g(n), then fl (n) (/2(n)). 10 points