Let

A

and

B

be sets of real numbers. Define a set

A+B

by\

A+B={a+b|ainA and binB}.

\ (a) Let

A={-1,0,3,5}

and

B={-2,12,20}

. Find

A+B

.\ (b) Show that if

A

and

B

are bounded sets, then\ l.u.b. l.u.b.

A

l.u.b.

B

\ and\ g.l.b. g.l.b.

A

g.l.b.

B

.\ (c) Define a set and

binB

. Give an example where\

g.l.b. (AB)!=( g.l.b. A) (g.1.b. B).

Let A and B be sets of real numbers. Define a set A+B by A+B={a+baAandbB}. (a) Let A={1,0,3,5} and B={2,12,20}. Find A+B. (b) Show that if A and B are bounded sets, then l.u.b. (A+B)=( l.u.b. A)+( l.u.b. B) and g.l.b. (A+B)=( g.l.b. A)+( g.l.b. B). (c) Define a set AB={abaA and bB}. Give an example where g.l.b.(AB)=(g.l.b.A)(g.l.b.B)