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Vinnie76
Group Title
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 ab).
b) R is the relation on Z where a R b if ab.
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.
 one year ago
 one year ago
Vinnie76 Group Title
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 ab). b) R is the relation on Z where a R b if ab. 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.
 one year ago
 one year ago

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Vinnie76 Group TitleBest ResponseYou've already chosen the best response.0
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 ab). b) R is the relation on Z where a R b if ab. 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).]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
I actually don't know what antisymmetric means, but I guess I can help out with the other ones... Let's start with (a)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Do you remember what 'reflexive' means?
 one year ago
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