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

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

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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

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