Consider the two following properties for binary relations:

a$)$ Are the two separate relationss "knows" and "sibling of$"$ among all people you know complete, reflexive, transitive, symmetric, and antisymmetric? If yes, prove why. If no$,$ give a counterexample. Explain.

Consider the properties of

irreflexivity: $,$AAainS,aRa does not hold,

negative transitivity: AAa,$b,$cinS, if notaRb and $]$ then $[$not aRc $]$

b$)$ Are the relationships and $"="$ irreflexive and$/$or negatively transitive on the set $Z?$ Explain.

c$)$ Take the binary relations Parent and Friend we analyzed in a table. Which of these relations is irreflexive or negative transitive, which is not? Explain.