If $||cdot||_{alpha}$ and $||cdot||_{beta}$ are norms, show that $max{||cdot||_alpha, ||cdot||_beta}$ is a norm. What about the min?

If $||cdot||_{alpha}$ and $||cdot||_{beta}$ are norms, show that $max{||cdot||_alpha, ||cdot||_beta}$ is a norm. What about the min?

How to solve this problem. Thanks for the help