Posted by Anonymous on .
Prove that if a subset C of R*R is symmetric with respect to both the xaxis and yaxis, then it is symmetric with respect to the origin

math 
MathMate,
Let x,y ∈ ℝ
(x,y) ∈ C
=> (x,y) ∈ C ..... symm. about yaxis
=> (x,y) ∈ C ..... symm. about xaxis
Prove similarly that
(x,y)∈C => (x,y) ∈C.
Thus,
(x,y)∈C <=> (x,y)∈C
or C is symmetric about the origin.