Read the statement and choose the letter pair that represents a conclusion…
2025
Read the statement and choose the letter pair that represents a conclusion that must follow. In an option XY, X is the premise and Y is the conclusion.
She chats on her mobile only when her boss is away for lunch.
A. The boss is away for lunch.
B. She did not chat on her mobile.
C. She chatted on her mobile.
D. The boss is not away for lunch.
Answer: A. DB — Concept: In a conditional statement of the form ‘X only when Y’, Y is a necessary condition for X, so the logical form is X → Y. Every conditional P → Q is…
- A.
DB
- B.
AB
- C.
DC
- D.
BC
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Show answer & explanation
Correct answer: A
Concept: In a conditional statement of the form ‘X only when Y’, Y is a necessary condition for X, so the logical form is X → Y. Every conditional P → Q is logically equivalent to its contrapositive ¬Q → ¬P; its converse and inverse are not guaranteed by the original statement.
Application: Let C mean ‘she chatted on her mobile’ and A mean ‘the boss is away for lunch’. Then B means ¬C and D means ¬A.
Translate the given sentence: ‘She chats only when her boss is away’ becomes C → A.
Form the contrapositive by reversing and negating both parts: ¬A → ¬C.
Replace ¬A with D and ¬C with B. This gives D → B, encoded by the pair DB.
AB means A → B. The premise only says A is necessary for C; it does not make A imply B.
DC means D → C. When the necessary condition A is absent, C cannot occur, so D does not imply C.
BC means B → C, or ¬C → C. That implication is not supplied by the statement.
Cross-check: Assume D is true, so the boss is not away for lunch. Because being away is necessary for chatting, she cannot have chatted; therefore B is true. This independently confirms the implication D → B and the pair DB.