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math

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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

  • math -

    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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