1.1.5 Syllogism and verbal reasoning notes

1. 1.1.5.1Syllogism: Venn method, possibility and either–or

   Take the statements as true even if they sound absurd, draw the smallest Venn diagram that fits them, and accept a conclusion only if it holds in every possible diagram; a possibility is accepted if at least one diagram allows it.

   Advanced · 8 min · Full course
2. 1.1.5.2Venn diagrams: relationships between classes

   A Venn question asks either how classes sit with respect to each other (inside, overlapping or apart) or how many members fall in a region; the first is answered by logic about the words, the second by the inclusion–exclusion formula.

   Advanced · 8 min · Full course
3. 1.1.5.3Statement and assumption

   An assumption is what the speaker must already believe for the statement to make sense; it is never written in the statement, and if you deny it the statement loses its point.

   Advanced · 8 min · Full course
4. 1.1.5.4Statement and conclusion, inference and course of action

   A conclusion must follow from the statement alone, with no outside facts; a course of action must be practical, follow from the problem and reduce it.

   Advanced · 8 min · Full course
5. 1.1.5.5Strength of arguments and cause–effect

   A strong argument is directly related to the question, gives a real and important reason, and does not rest on opinion or exaggeration; in cause–effect pairs, decide which event could produce the other, or whether both come from something else.

   Advanced · 8 min · Full course
6. 1.1.5.6Logical connectives: if–then, only if, unless, necessary and sufficient conditions

   Turn every sentence into an arrow P → Q; the only safe moves are forward (P, so Q) and backward through the contrapositive (not Q, so not P); knowing Q or knowing not P tells you nothing.

   Advanced · 9 min · Full course
7. 1.1.5.7Truth-tellers and liars

   Assume one person's type (or one suspect), work out what every statement must then be, and keep only the case with no contradiction; two statements that contradict each other split the true and the false between them.

   Advanced · 8 min · Full course
8. 1.1.5.8Inequalities: direct and coded (≥, >, either–or)

   Read the chain between the two terms you are asked about: if all the signs point the same way, a conclusion follows (strict if any sign is strict); if the signs point opposite ways anywhere between them, nothing follows.

   Advanced · 7 min · Full course
9. 1.1.5.9Critical reasoning: strengthen, weaken and assumptions in a passage

   Split the passage into evidence and conclusion, find the gap between them, and then pick the option that fills the gap (assumption), widens it (weaken) or narrows it (strengthen).

   Advanced · 9 min · Full course
10. 1.1.5.10Inference from passages: definitely true, probably true, false

    An inference is what the passage makes certain or likely without saying it in so many words; grade each option by how far it is from the text: forced by it, leaning with it, not touched by it, leaning against it, or contradicted by it.

    Advanced · 8 min · Full course
11. 1.1.5.11Decision making and problem solving: rule-based and situation questions

    Rule-based questions are a checklist: test every condition, apply an exception only when it exactly fits, and answer "data inadequate" when a needed fact is missing; situation questions reward the response that solves the problem lawfully, fairly and without passing the buck.

    Advanced · 8 min · Full course
12. 1.1.5.12Logical sequence of words and order of events

    Find the thread that orders the words (time, growth, process, size or rank, or plain alphabetical order), fix the first and last items, then slot the middle ones; check the options instead of writing out the whole sequence.

    Advanced · 7 min · Full course

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