Posted by **Anonymous** on Tuesday, January 11, 2011 at 3:28am.

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

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**MathMate**, Tuesday, January 11, 2011 at 7:15pm
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.

Thus,

(x,y)∈C <=> (-x,-y)∈C

or C is symmetric about the origin.

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