Is this a Function?

📌 CONCEPT: A relation R on a set A is considered a function if and only if each element in the domain (set A) is associated with exactly one element in the codomain (set B), i.e., no element in set A has multiple mappings.

📐 RULE / FORMULA: A relation R on A is a function if for every a in A, there exists at most one b in B such that (a, b) ∈ R.

💡 WORKED EXAMPLE: Let's consider the given relation R = {(1, 3), (2, 5), (3, 5), (4, 3)} on the set A = {1, 2, 3, 4}. We can see that each element in set A has a unique mapping in set B. For example, the element 1 is mapped to 3, 2 is mapped to 5, 3 is mapped to 5, and 4 is mapped to 3. This satisfies the condition of being a function.

⚠️ COMMON MISTAKE: Many students make the mistake of assuming that a relation is a function if it has at least one mapping. However, a relation can still be a function even if it has multiple mappings, as long as each element in the domain has at most one mapping in the codomain.