Convexity of set A = {(x,y) in R^2  x^4+y^4 =< 1, x>=0
How can I show that the set A = {(x,y) in R^2  x^4+y^4 =< 1, x>=0 y>=0} is convex.

I am sure it can be shown by definition, but I propose an easy way (not rigorous though)
The function is (weakly) convex The lower contour set (=<1) of a convect function is convex. 
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