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

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 both have the property. For each of Rc, 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 a proof. Any time you answer Statement ii, provide two examples: one where the new relation has the property, and onewhere the new relation does not. (You may use graphs to describe your examples.)
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