Many Logical Reasoning questions turn on rules. Translate each rule into an arrow, chain the arrows, and use only the contrapositive to go backward.
| If A, then B | A → B |
|---|---|
| A only if B | A → B |
| Not A unless B | A → B |
| Every A is B | A → B |
| No A is B | A → not B |
From A → B you may conclude not B → not A, the contrapositive. Nothing else runs backward.
If the museum receives the grant, it will extend its weekend hours. The museum will extend its weekend hours only if it hires more guards. The museum will never hire more guards.
If the statements above are true, which one of the following must also be true?
Unless the river is below flood level, the ferry will not run. The river is below flood level only if there has been no heavy rain this week.
If the statements above are true and the ferry is running, which one of the following must be true?
Every painting hanging in the north gallery belongs to the museum's collection and was painted before 1900. Every painting in the museum's collection that was painted before 1900 has been cleaned in the past ten years.
If the statements above are true, which one of the following must also be true?
'A only if B' says B is required for A. So whenever A happens, B has happened: A → B.
'Not A unless B' means A requires B, so A → B. Read 'unless' as 'if not'.
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