Mathematics Homework Solutions
#18401
Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive
Determine whether the binary relation R on Z, where aRb means a^2 = b^2, is reflexive, symmetric, antisymmetric, and/or transitive.
A binary relation is examined as to whether it is reflexive, symmetric, antisymmetric, and/or transitive. The solution is concise but thorough.
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- Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive - Determine whether the binary relation R on Z, where aRb means |a-b| <= 1, is reflexive, symmetric, antisymmetric, and/or transitive.
- Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive - Consider the following relation R on the set of positive integers: R = {(x,y)|gcd(x,y)} = 1 Is this relation reflexive, symmetric, antisymmetric, and/or transitive?
- List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric. - List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric
- Binary Relations : Reflexive, Symmetric, Antisymmetric, and/or Transitive - Consider the following relation R on the set of positive integers: R = {(x,y)|x and y have the same prime divisors} Is this relation reflexive, symmetric, antisymmetric, and/or transitive?
- Binary Relations : Reflexive and Transitive, but not Antisymmetric - Give an example of or else prove that there are no relations on {a,b,c} that is reflexive and transitive, but not antisymmetric.
