18. Let S be a set of real numbers such that l.u.b.(S) = 5/6 and g.l.b.(S) = 1/3, and let T = {-3x/2 | x belongs to S}. Then l.u.b.(T) =

 

A. –3/2

B. –5/4

C. –5/9

D. –1/2

E. –4/9

 

Solution: The answer is D

 

Given the least upper bound and the greatest lower bound of the set S, then any element x that belongs to S satisfies the following inequality,

Thus, to find the least upper bound of T, multiply the above inequality by –3/2, so that,

 

This new inequality shows that the least upper bound of T is –1/2.