1. Let S1={X^2 : X is real number} and S2= {X^2 : X is real number, X not equal to 0}.
a) Show that the binary operations + ,．on real number restrict to binary operations on S1 and on S2.
b) Which of the structures (S1,+), (S2,+),(S1,．),(S2,．) is a group? For each case for which it isn't a group, explain which group properties fail to hold.