problemset1 - X where x y and y z , we have x z . Question...

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Introduction to Economic Analysis NYU, Fall 2010 Luke Geldermans Problem set 1 Selected defnitions ±rom maths review The cartesian product , written X × Y , of two sets X and Y is the set of all ordered pairs where the Frst element is taken from X and the second from Y : X × Y = { ( x, y ) : x X and y Y } . A binary relation R on a set X is a subset of X × X . (This deFnition is quite abstract, don’t worry if it takes some time to get your mind around it.) A binary relation on X is refexive if for all x X , we have x x . A binary relation on X is symmetric if for all x, y X where x y , we have y x . A binary relation on X is transitive if for all x, y, z
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Unformatted text preview: X where x y and y z , we have x z . Question 1 Prove that ( A B ) c = A c B c . Question 2 Let X be a set of people. Do the following describe binary relations on X ? a) is an ancestor oF b) is a Family c) is the opposite sex to d) is at least as old as e) is Female f) is the same sex as g) is a blood relative to (ie. shares a common ancestor) or those that do describe binary relations on X , which of the properties refexivity , sym-metry and transitivity hold?...
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This note was uploaded on 03/25/2011 for the course ECON 006 taught by Professor Bisin during the Spring '11 term at NYU.

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