DSE 2016 Q17

Posted by eco'17 on Mar 22, 2017; 7:06am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2016-Q17-tp7603515.html

Consider a set {(x,y) R+ X R| Y<= lnx-e^x}. This set is:
(a) a linear subspace of R2=x
(b) convex
(c) convex and a linear subspace of R2
(d) neither convex, nor a linear subspace of r2

while I know that the given set is not a linear subspace of R2 because this will will not contain 0 vector, because lnx and e^x being symmetric along y=x will not intersect each other, but I don't know how to work for convexity of the set.
i know the definition but I don't know how to apply that
please help
thanks in advance!