Directions: Questions below are to be answered on the following data. A causes…
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Directions: Questions below are to be answered on the following data.
A causes B or C, but not both, F occurs only if B occurs, D occurs if B or C occurs, E occurs only if C occurs, J occurs only if E or F occurs, D causes G, H but not both, H occurs if E occurs, G occurs if F occurs.
If B occurs which must occur?
Answer: A. D — ConceptIn conditional logic, “X if Y” means Y → X, while “X only if Y” means X → Y. A necessary consequence must follow in every scenario that satisfies all…
- A.
D
- B.
D and G
- C.
G and H
- D.
F and G
Attempted by 73 students.
Show answer & explanation
Correct answer: A
Concept
In conditional logic, “X if Y” means Y → X, while “X only if Y” means X → Y. A necessary consequence must follow in every scenario that satisfies all the rules; an implication cannot be reversed.
Application
Translate the direct rule: “D occurs if B or C occurs” means (B or C) → D.
The question gives B. Therefore the antecedent B or C is true, and modus ponens gives D.
“F occurs only if B occurs” means F → B, not B → F. Thus B alone does not force F; without F, the rule F → G does not force G.
The rule from D gives exactly one of G and H. It does not determine which branch occurs, so neither G nor H is individually guaranteed.
Cross-check and contrast
A consistent test case is B, D, and H occurring while C, E, F, G, and J do not occur. Every relevant implication and the exclusive G/H split is satisfied.
D follows from the direct implication whose antecedent is B or C.
D and G adds G, but the implication F → G does not make G follow from B when F has not been established.
G and H conflicts with the rule that exactly one of them follows D.
F and G assumes F from B by reversing the “only if” implication.
Result
Therefore, the event that must occur is D.