Logical Reasoning
Logical Reasoning tests the validity of inference rather than the truth of the content: syllogisms, statement and assumption, cause and effect, course of action, strong and weak arguments, and coded inequalities.
Syllogisms
Draw the minimum diagram consistent with the premises, then ask whether the conclusion must hold in every such diagram. Rules: All A are B converts to Some B are A; Some A are B converts to Some B are A; No A is B converts to No B is A; All A are B does not convert to All B are A. Two particular premises yield no conclusion.
Assumption and argument questions
An assumption is unstated and necessary; negate it and see whether the argument collapses. A strong argument is relevant to the stated issue and materially supports or attacks it; emotional language does not make an argument strong.
Coded inequalities
Chain symbols in one direction only. From A > B and B >= C you get A > C, but no fixed relation between A and C beyond that.
Worked example
All engineers are graduates. Some graduates are managers. Conclusions: I. Some engineers are managers. II. Some graduates are engineers.
Premise one converts validly to II, so II follows. For I, the managers who are graduates may lie outside the engineer set, so it is not forced. Only II follows.
Traps
- Assuming some means some but not all; in logic, some includes all.
- Illicit conversion of All A are B into All B are A.
- Judging a conclusion by real-world plausibility instead of the premises.
- Accepting a restatement of the premise as an assumption.
- Treating a popular belief or an emotional appeal as a strong argument.