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Difficulty: EasyIdentifying Must-Be-True Statements and Valid Deductions

During the annual performance review, every project manager who met their sales target received a performance bonus. Furthermore, any manager who received a performance bonus was granted extra vacation days.

Evaluate the following statement based strictly on the information above:
If a project manager did not receive extra vacation days following the annual performance review, that project manager did not meet their sales target.

Answer: Answer

Answer

True
The statement represents a valid contrapositive deduction. By combining the two premises (Target Met → Bonus and Bonus → Extra Vacation), we deduce that meeting the target guarantees extra vacation days. The contrapositive (lacking extra vacation days guarantees the target was not met) must therefore be true.

Step-by-Step Solution

1
Identify and formalize the conditional statements given in the passage.
Premise 1: Target Met → Bonus. Premise 2: Bonus → Extra Vacation.
Converting natural language into formal conditional statements clarifies logical relationships.
2
Chain the conditional premises together.
Target Met → Extra Vacation.
If statement A implies statement B, and statement B implies statement C, then statement A logically guarantees statement C.
3
Form the contrapositive of the chained conditional statement.
NOT Extra Vacation → NOT Target Met.
The contrapositive of a valid conditional statement is always logically equivalent and must be true.

Key Concept

Identifying Must-Be-True Statements and Valid Deductions
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Identifying Must-Be-True Statements and Valid Deductions

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