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# Discrete Math: Binary Relations

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SECTION 10.2

For #2: A binary relation is defined on the set A = {0, 1, 2, 3}. For the relation given,
a. draw the directed graph (See drawing tips in the Overview)
b. determine whether the relation is reflexive
c. determine whether the relation is symmetric
d. determine whether the relation is transitive
Give a counterexample in each case in which the relation does not satisfy one of the properties.

2. R2 = {(0,0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}

16. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers.
F is the congruence modulo 5 relation on Z: for all m, n &#61646; Z, m F n &#61659; 5 | (m - n).
Hint: Model your work on the examples in the Important Points discussion of section 10.2 or on Example 10.2.5 on pages 552-553. [When justifying your answer for each property, either include a discussion OR a formalized proof. It is not required to do both a discussion and a proof, as the textbook does in its example.]

24. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers. (Brief explanations are all that's required.)
Let X = {a, b, c} and P(X) be the power set of X. A binary relation R is defined on P (X) as follows:
for all A, B &#61646; P (X), A R B &#61659; n(A) < n(B) (that is, the number of elements in A is less than the number of elements in B.

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2. a. Please see the following graph.

b. No. Since
c. No. Since , but
d. No. Since ...

#### Solution Summary

Binary relations are graphed and their properties determined. The relation of reflexive and symmetric is determined.

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