Let || ||1 and || ||2 be two different norms on a vector space V.

Question:

Let || • ||1 and || • ||2 be two different norms on a vector space V.
(a) Prove that ||v|| = max{ ||v||1. ||v||2} defines a norm on V.
(b) Does ||v|| = min{ ||v||1. ||v||2} define a norm?
(c) Does the arithmetic mean
||v|| = 1/2(||v||1 + ||v||2)
define a norm?
(d) Does the geometric mean
||v|| = √||M||, ||v||2
define a norm?