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Math Help - Restriction of a Set

  1. #1
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    Restriction of a Set

    My professor defined the restriction of a set:
    R is a relation X. and Y is a subset of X.
    all ordered pairs (x,x') that are elements of Y X Y such that xRx'.

    What would be the restriction to the subset of positive real numbers for the relation xRy if x^2 + y^2 = 1?

    I am kind of unsure exactly what this restriction means.
    Last edited by Snooks02; April 12th 2009 at 06:22 PM.
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  2. #2
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    Restriction of a set

    Hello Snooks02
    Quote Originally Posted by Snooks02 View Post
    My professor defined the restriction of a set:
    R is a relation X. and Y is a subset of X.
    all ordered pairs (x,x') that are elements of Y X Y such that xRx'.

    What would be the restriction to the subset of positive real numbers for the relation xRy if x^2 + y^2 = 1?

    I am kind of unsure exactly what this restriction means.
    Suppose X is the set {1, 2, 3, 4} and R is the relation on X: xRy if and only if x > y.

    Then R = {(2, 1), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)}

    Suppose now that we define a subset Y as {1, 2, 3}.

    Then Y x Y = {(1, 1), (2, 1), (3, 1), (1, 2), (2, 2), (3, 2), (1, 3), (2, 3), (3, 3)}

    So the restriction of R to Y is those elements (ordered pairs) of R that are also elements of Y x Y; in other words {(2, 1), (3, 1), (3, 2)}.

    So, in the question you are given, instead of all values of x and y (positive and negative) that satisfy x^2 + y^2 = 1 you need only those that are positive. On a Cartesian (x-y) plane, instead of the whole circle centre O, radius 1, we just get the quarter of this circle that lies in the first quadrant. OK?

    Grandad
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