Performance Objective Demonstration

PO#$6$ Determine whether a given binary relation is a linear order, partial order, or equivalence relation.

Write thorough work for each prompt.

Give an example of a partial order on the set $\{a,b,c,d\}$ that contains $(a,b)$ and $(b,d)$ that is NOT a linear order. Provide a detailed explanation of why your example demonstrates a partial order and why it is not a linear order.

Note: you may give your example as the set of ordered pairs, a directed graph, or a matrix.