The binary relation "less than or equal to" is defined on the set Represent it in roster form.
Solution.
We list all ordered pairs that satisfy the relation definition:
Example 2.
The binary relation "greater than" is defined on the set Represent it in roster form.
Solution.
Given that
we list the elements of the set in increasing order:
Now we can build the ordered pairs satisfying the relation "greater than":
Example 3.
Let Represent the relation on the set in matrix form.
Solution.
The logical matrix represents all ordered pairs on the set If an element of the matrix (an ordered pair) satisfies the condition it is labeled by If not, it is labeled by
Figure 5.
Example 4.
Let Represent the divisibility relation on the set as a matrix.
Solution.
The entry of the logical matrix is set to be equal to if the element of the row divides the element of the column. Otherwise, the entry is zero.
Figure 6.
Example 5.
The relation on the set is given by the matrix
Represent using a digraph.
Solution.
The digraph contains nodes and directed edges. The number of nodes is equal to the cardinality of the set and the number of edges is equal to the number of matrix elements with value
Figure 7.
Example 6.
Let A relation on the set is defined as follows:
Draw the digraph of
Solution.
To satisfy the divisibility condition the sum of the components and must be even. Hence, the relation includes the following ordered pairs:
The directed graph of the divisibility relation looks as follows:
