Is the set {(x,y) | x^4+y^4 ≤ 1, x≥0, y≥0} convex?

[peteryellow]

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

 

[CHatUPenn]

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.