Which of the followings are norms on $\mathbb R^2 ?$

Question

1. $||x||_1=|x_1|+|x_2|$, where $ x=(x_1,x_2)\in \mathbb R^2$

2. $||x||_2=\displaystyle\sqrt {x_1^2+x_2^2}$, $ x=(x_1,x_2)\in \mathbb R^2$

3. $ ||x||_{max}=max\{||x||_1,||x||_2\}$,$ x=(x_1,x_2)\in \mathbb R^2$

4. $||x||_{min}=min\{||x||_1,||x||_2\}$ ,$ x=(x_1,x_2)\in \mathbb R^2$

I know that 1,2 are true as satisfy all conditions of norm, how to prove or disprove 3,4 ?

Thanks.