Khan.randRange(0,5) ["isFatherOf on the set of people", "isAncestorOf on the set of people", "isOlderThan on the set of people", "isSisterOf on the set of people", katex.renderToString("\\{ \\langle 2,1 \\rangle , \\langle 1,3 \\rangle , \\langle 2,3 \\rangle \\}") + " on the set " + katex.renderToString("\\{1,2,3\\}"), katex.renderToString("\\{ \\langle a,b \\rangle , \\langle a,a \\rangle , \\langle b,a \\rangle \\}") + " on the set " + katex.renderToString("\\{a,b\\}")] ["False", "True", "True", "False", "True", "False"]

Does the following relation define a partial ordering on the indicated set?

CHOICES[CHOICESINDEX]

ANSWER[CHOICESINDEX]
  • "True"
  • "False"

A relation is a partial ordering if it is antisymmetric and transitive.

Is the relation antisymmetric on the set? That is, for any two elements a and b of the set, if (a, b) is in the relation, then (b, a) is NOT in the relation?

Is the relation transitive on the set? That is, for any three elements a, b, and c, if (a, b) is in the relation and (b, c) is in the relation, then is (a, c) also in the relation?