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For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following. Assume that R...

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Advance Math

For each of the properties reflexive, symmetric, antisymmetric,and transitive, carry out the following.

Assume that R and S are nonempty relations on a set A that bothhave the property. For each of R complement, R?S, R?S, and R?1,determine whether the new relation

  1. must also have that property;
  2. might have that property, but might not; or
  3. cannot have that property.
  4. A ny time you answer Statement i or Statement iii, outline aproof. Any time you answer Statement ii, provide two examples: onewhere the new relation has the property, and onewhere the newrelation does not.

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