Notethat this chaincouldbe extendedwith additionallinks.
Let be the relation“is the motherof.” Let be the relation“is the brotherof.”
8.Is symmetric?Explainyour answer.
- Is symmetric?Explainyour answer.
- Is transitive?Explainyour answer.
- Is transitive?Explainyour answer.
- Let and be real numbers.Prove:If and , then
- The followingstatementisnottrue.“Let and be points.If and
, then ” Drawa diagramwith thesepointsshownto providea counterexample.Answers
1.
2.
3.
4.
5.
- ( or ).
- If and then (transitiveproperty).If and then (transitive
property).If and then (transitiveproperty).
- No. If Mariais the motherof Juan,it doesNOTfollowthat Juanis the motherof Maria!
- Yes. For example,if Bill is Frank’s brother, then Frankis Bill’s brother.
- No. If weretransitive,then “Mariais Fern’s motherand Fern is Gina’s mother”wouldlead to “Maria
is Gina’s mother.” However, Mariawouldactuallyhaveto be Gina’sgrandmother! - Yes. If Bill is Frank’s brotherand Frankis Greg’s brother, the Bill is Greg’s brother. You mightsay the
brotherof my brotheris (also)my brother. - and (given); (reflexive); (substitute for and
for ). - Belowis an example: