Answer:
see below
Explanation:
There are some subtleties here.
Drawing conclusions
When conclusions are drawn based on patterns, it is called inductive reasoning. When those conclusions are drawn based on facts, it is called deductive reasoning.
Theories and proofs
When a pattern is observed, it gives rise to a conjecture. If there is a counterexample, then the conjecture must be declared false. If an argument can be made based on logic, then the conjecture is said to have a proof. A proven conjecture (statement) can then be referred to as a theorem.