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
asked Aug 17, 2013 in Algebra 1 Answers by MAAN

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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 ≠ {}

answered Oct 29, 2015 by Fermat Level 10 User (61,380 points)

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