To list the ordered pairs, we must follow the condition stated in the relation.

In this case, (a,b) ∊R if a divides b. In other words, when we divide b by a, we get as a result an integer value, and the remainder is 0.

a) List all the ordered pairs in the relation R = {(a,b) | a divides b} on the set {1,2,3,4,5,6}

(1,1), (1,2),(1,3), (1,4), (1,5), (1,6), (2,2), (2,4), (2,6), (3,3), (3,6), (4,4), (5,5), (6,6)

The following two questions refer to a figure from the textbook. To make it easy for you, I’ll share the figure below.

b) Display this relation graphically, as was done in Example 4.

c)Display this relation in tabular form, as was done in Example 4

Related exercises:

• Give an example of a relation on a set that is a) both symmetric and antisymmetric. b) neither symmetric nor antisymmetric
• Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive
• Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y)∈R if and only if
• Show that the relation R=∅ on the empty set S=∅ is reflexive, symmetric, and transitive
• Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only if