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*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 ≠ {}**

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