# 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