Logical Reasoning and Problem Solving
What this domain tests
Logical Reasoning and Problem Solving tests structured thinking: deductive conclusions, conditional ('if–then') rules, syllogisms, ordering and scheduling, and identifying assumptions or flaws. Police work uses these skills when applying policy, sequencing an investigation, and testing whether a conclusion is supported.
Core rules
- Valid conditional forms: From 'If P, then Q' and P, conclude Q (modus ponens). From 'If P, then Q' and not Q, conclude not P (modus tollens).
- Invalid forms: From Q, do not conclude P (affirming the consequent). From not P, do not conclude not Q (denying the antecedent).
- 'Only if' reverses the arrow: 'P only if Q' means P → Q.
- 'Unless' means 'if not': 'P unless Q' means not Q → P.
- In ordering problems, build a grid or list and place fixed items first.
- Separate necessary from sufficient. A requirement is not a guarantee.
Worked example
Rule: 'If a report is late, it is flagged for review. All flagged reports are audited.' Fact: 'Report 14 was not audited.' What follows? Reasoning: Flagged → audited. Report 14 was not audited, so by modus tollens it was not flagged. A report is late → flagged; not flagged, so not late. Conclusion: Report 14 was not late. The invalid move is to conclude from 'not audited' something about being flagged directly without using the chain; the valid conclusion is 'not late.'
Traps that cost marks
- Reversing 'if–then' statements.
- Treating 'some' as 'all.'
- Assuming that because two events co-occur, one caused the other.
- Ignoring a second rule that changes the chain.
- Choosing an answer that is possible but not forced.