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Vinnie76

  • 2 years ago

For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. a) R ⊆ Z+ X Z+ where a R b if a|b). b) R is the relation on Z where a R b if a|b. c) For a given universe U and a fixed subset C of U, define R on P (U) as follows: For A, B ⊆ U we have A R B if A ∩ C = B ∩ C. d) On the set A of all lines in R2, define the relation _ for two lines _1, _2 by _1 _ _2 if _1 is perpendicular to _2. e) R is the relation on Z where x _ y if x + y is odd. f ) R is the relation on Z where x _ y if x − y is even.

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  1. Vinnie76
    • 2 years ago
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    For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. a) R ⊆ Z+ X Z+ where a R b if a|b). b) R is the relation on Z where a R b if a|b. c) For a given universe U and a fixed subset C of U, define R on P (U) as follows: For A, B ⊆ U we have A R B if A ∩ C = B ∩ C. d) On the set A of all lines in R2, define the relation _ for two lines _1, _2 by _1 _ _2 if _1 is perpendicular to _2. e) R is the relation on Z where x _ y if x + y is odd. f ) R is the relation on Z where x _ y if x − y is even. g) Let T be the set of all triangles in R2. Define R on T by t1 R t2 if t1 and t2 have an angle of the same measure. h) R is the relation on Z X Z where (a, b)_(c, d) if a ≤ c. [Note: R ⊆ (Z X Z) X(Z X Z).]

  2. terenzreignz
    • 2 years ago
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    I actually don't know what antisymmetric means, but I guess I can help out with the other ones... Let's start with (a)

  3. terenzreignz
    • 2 years ago
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    Do you remember what 'reflexive' means?

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