Homework for February 14, 2019: Due TUESDAY February 19.
1. Recall the definitions of reflexive, symmetric and transitive relations.
Recall that a relation is a set of ordered pairs.
Let A = {1,2,3}.
For each of the following, create digraphs and the resultant set of order pairs
that show the following:
(a) an example of a binary relation R1 over A that is
reflexive but not symmetric, but not transitive.
(b) provide an example of a binary relation R2 over A that is
not reflexive and not transitive, and not symmetric.
(c) provide an example of a binary relation R3 over A that is
not reflexive and is symmetric and transitive.
2. Complete the answers from page 6 on the 08-RelationsDeepDive lecture slide.
It will help to draw the digraphs.
3. Determine the relations for a, b in the set of integers and the mathematical
relation R: >, i.e "greater than"
4. Determine the relations for a, b in the set of integers and the mathematical
relation R: a*b = 0