Final answer:
The expression for s o s in ordered pair notation is s o s = (a, b) ∈ s and (b, c) ∈ s.
Explanation:
The composition of relations, denoted as s o s, involves combining two relations, where the resulting relation consists of ordered pairs that connect elements from the first relation to elements in the second relation.
In ordered pair notation, s o s = (a, c) , which signifies that for any ordered pair (a, c) in the composed relation, there exists an intermediary element 'b' such that (a, b) is in s and (b, c) is also in s. This notation implies the linkage between elements a and c through a common intermediary 'b' within the relation s.
Essentially, it captures the combined connections between elements in the original relation s, showing the path from the initial element 'a' to the final element 'c' via the intermediate element 'b' existing in relation s.
The expression elucidates the process of linking pairs from the original relation to form a new relation based on shared elements within the set. This composition creates a new relation that reflects the transitive connections between elements in the set, illustrating how elements are related to each other based on the rules defined by the relation s.