Assignment:
Q1. 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.
Q2. R2 = {(0,0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}
Q3. 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 ∈ Z, m F n ↔ 5 | (m - n).
Q4. 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 ∈ P (X), A R B ↔ n(A) < n(B) (that is, the number of elements in A is less than the number of elements in B.
Provide complete and step by step solution for the question and show calculations and use formulas.