Consider the following statements:
P: Combinatorics is always invoked in the modeling of physical phenomena.
Q: Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities.
Based on the passage above, what can be inferred about statements P and Q?
B
Step-by-Step Solution
Insight: Statement evaluation requires checking if the wording in the option strictly matches the passage without generalizing moderate quantifiers (like "sometimes") to absolutes (like "always").
Exam route: Statement P uses "always", but the passage uses "sometimes" for combinatorics in physical models. Thus P is False. Statement Q uses "some", which is logically entailed by the passage's "Often, in such models". Thus Q is True. Match with Option B.
Learning route:
- Analyze P: The passage explicitly states, "This kind of counting is sometimes used in the modeling of several physical phenomena." Statement P claims, "Combinatorics is always invoked". "Always" contradicts "sometimes". Therefore, P is False.
- Analyze Q: The passage states, "Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities." Statement Q claims, "Modeling some physical phenomena involves assigning probabilities...". Since "often" implies that it happens in at least some cases, "some" is a necessary truth derived from the text. Therefore, Q is True.
- Conclusion: P is False and Q is True. Option B correctly reflects this.