Let

A={x+y\\\\sqrt(2)|x,yinQ}subeR

.\ (a) Prove that for all

x,yinQ,x+y\\\\sqrt(2)=0

if and only if

x=y=0

.\ (b) Prove that for all

z_(1),z_(2)inA,z_(1)+z_(2),z_(1)z_(2)inA

and, for

z_(2)!=0,(z_(1))/(z_(2))inA

.

7. Let A={x+y2x,yQ}R. (a) Prove that for all x,yQ,x+y2=0 if and only if x=y=0. (b) Prove that for all z1,z2A,z1+z2,z1z2A and, for z2=0,z2z1A