Logical Reasoning
Logical Reasoning tests formal thinking: whether a conclusion follows necessarily from the statements given, not whether it sounds true in the real world.
Core rules
- Categorical statements: All A are B; No A are B; Some A are B. Diagram them with overlapping circles before choosing.
- Conditional statements: "If P then Q" allows only two valid moves - affirm P (so Q), or deny Q (so not P). Denying P or affirming Q proves nothing.
- Contrapositive: "If P then Q" is equivalent to "If not Q then not P."
- Only if and unless: "P only if Q" means if P then Q; "unless Q, P" means if not Q then P.
- Ordering items: draw a line or grid; never hold the constraints in your head.
- Assumptions: the unstated premise the argument needs, not a restatement of the conclusion.
Worked example
If a recruit passes the physical test, then he advances to the interview. Recruit Cruz did not advance to the interview. What follows? Let P = passes physical test, Q = advances to interview. You are given P → Q and not Q. By modus tollens, not Q → not P, so Cruz did not pass the physical test. The invalid move would be to conclude something about recruits who did advance, or to deny the antecedent.
Traps that cost marks
- The converse error: "If P then Q" does not give "If Q then P."
- Treating "some" as "some but not all," or assuming "all" guarantees a named individual exists.
- Importing real-world facts into syllogisms that define their own terms.
- Confusing "no A are B" with "not all A are B."