Final answer:
The concept in question is mutually exclusive events in probability, where two events cannot occur simultaneously. The response provides understanding within the realm of mathematics and addresses the condition of avoiding false premises as per Harman's theory.
Step-by-step explanation:
The question revolves around the concept of mutually exclusive events in probability theory. Mutually exclusive events are ones that cannot happen at the same time. The scenario presents two situations with events R, P, Q, and H, and desires to know if certain pairs are mutually exclusive.
In response to whether events F and G are mutually exclusive, you can refer to a given solution that states 'if A has occurred, it is impossible to obtain two tails.' This implies that if one event occurs, the other cannot, meaning F and G are indeed mutually exclusive. The situation is the same for J and H. The premise states that J is the event of getting all tails. If you are considering a single coin toss, J and H are mutually exclusive because if one occurs, the other cannot.
An important aspect of understanding when inferring whether two events are mutually exclusive is to avoid any false premises as suggested by Harman's condition of 'no false lemmas' for Justified True Belief. Any belief that is based on a false premise (false lemma) would not be considered knowledge according to this theory. Therefore, evaluating the mutual exclusivity of events must exclude any inference based on falsehoods.