Let S be the set of people in the United States. Test the following binary relat

Question

Let S be the set of people in the United States. Test the following binary relations on S for reflexivity, symmetry, antisymmetry, and transitivity. xRy x is taller than y Reflexive: Symmetric: Antisymmetric: Transitive: xRy x has the same parents as y Reflexive: Symmetric: Antisymmetric: Transitive:

Explanation / Answer

(1) We can interpret a "taller than" b to be an ordering a > b on heights, which satisfies only the property of transitivity. For example, if Adam (say 6'2'') is taller than Bill (5'10''), and Bill is taller than Charles (5'6''), then Adam must definitely be taller than Charles. If we allow "taller than" to include equal heights, the relation would also satisfy reflexivity and anti-symmetry. (2) We can interpret "has the same parents as" to be an equivalence relation on people, so that the properties of reflexivity, symmetry, and transitivity are satisfied.

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