A={(x,y):y=ex,x is real},B={(x,y):y=e-x,x is real},then options
a)A intrsectionB={},
b)Aintersection B not equal to {},
c)Aunion B=R2
I'm assuming that set B should have y = e^(-x), and not y = e-x.
A intersection B is the single point (0,1).
This is the only point common to both sets.
Since (0,1) is not the null set, {}, then option a) is invalid and option b) is valid.
A union B is the set of all points satisfyng either y1 = e^x or y2 = e^(-x), but since R2 is the set of all possible ordered pairs, not just those satisfying y1 or y2, then option c) is invalid.
Answer: option b) - A ∩ B ≠ {}