Final answer:
The type of proof used to determine that m is even in an equation cannot be concluded without specific context, but the nature of various proofs such as direct, indirect, contradiction, mathematical induction, and deductive can be discussed.
Step-by-step explanation:
The type of proof used to determine that m is even in the equation p cannot be directly inferred from the question as it lacks the specific details or context of the proof itself. However, we can discuss the nature of each proof option provided:
- Direct Proof: It directly shows that a statement follows logically from other true statements.
- Indirect Proof (also known as Proof by Contradiction): It assumes that the statement to be proven is false and derives a contradiction from that assumption.
- Contradiction Proof: A form of indirect proof where the negation of the statement to be proven is shown to be contradictory.
- Mathematical Induction: It proves a statement is true for all natural numbers by proving it for the base case, and then proving that if it is true for an arbitrary case, it is true for the next case.
- Deductive Proof: It uses general premises or axioms to reach a specific, logical conclusion.
Given the options, deductive reasoning and a suggestion (or hypothesis) are terms closely related to the nature of the proofs mentioned. Additionally, when examining the probability of events, you can check if events are mutually exclusive or independent by calculating such probabilities in various ways, like P(G OR E) and P(G AND E).