Posted by Anonymous on .
Prove that if a subset C of R*R is symmetric with respect to both the x-axis and y-axis, then it is symmetric with respect to the origin
Let x,y ∈ ℝ
(x,y) ∈ C
=> (-x,y) ∈ C ..... symm. about y-axis
=> (-x,-y) ∈ C ..... symm. about x-axis
Prove similarly that
(-x,-y)∈C => (x,y) ∈C.
(x,y)∈C <=> (-x,-y)∈C
or C is symmetric about the origin.