AILET Logical Reasoning Syllabus

What does it mean for an argument to be 'valid' versus 'sound'?

Valid means the conclusion logically follows from the premises regardless of their truth. Sound means the argument is valid and all its premises are actually true, guaranteeing a true conclusion.

In critical reasoning, what is an assumption and how does it differ from a premise?

A premise is a reason that is explicitly stated. An assumption is an unstated belief the author takes for granted, which must be true for the argument to hold; it is the missing link between premise and conclusion.

What is the difference between an inference and a conclusion drawn from a passage?

A conclusion is the author's main stated point. An inference is something not explicitly said but that logically and necessarily follows from the given statements; it must be true if the statements are true.

What test determines whether a statement is a valid inference from a passage?

A valid inference must be necessarily true given the passage's information alone, without adding outside knowledge or going beyond what is stated. If the passage could be true while the statement is false, it is not a valid inference.

In statement-and-conclusion questions, what does 'the conclusion follows' require?

The conclusion must be logically derivable from the given statement(s) only, without assuming extra facts. If it requires outside information or merely could be true, it does not 'follow'.

What is the distinction between a cause and an effect in cause-and-effect reasoning?

The cause is the event or factor that produces a change; the effect is the resulting change that occurs because of the cause. The cause precedes the effect in time.

What is the post hoc fallacy in cause-and-effect reasoning?

Post hoc ergo propter hoc: assuming that because event B followed event A, A must have caused B. Mere temporal sequence or correlation does not establish causation.

In analogy questions, what is the core skill being tested?

Identifying the precise relationship between the first pair of terms and applying that same relationship to find the matching term for the second pair (e.g., type-of, part-of, cause-effect, function, degree).

How do you solve an analogy of the form 'A : B :: C : ?'

Determine the exact logical relationship from A to B, then find the term that bears the identical relationship to C in the same direction and at the same level of specificity.

What are the four standard categorical statement types used in syllogisms (A, E, I, O)?

A = universal affirmative ('All S are P'); E = universal negative ('No S is P'); I = particular affirmative ('Some S are P'); O = particular negative ('Some S are not P').

What is the basic method for solving syllogisms using Venn diagrams?

Draw circles for each term, shade regions emptied by universal statements and place an X for particular statements, then check whether each conclusion is necessarily depicted in every valid diagram.

From the premises 'All A are B' and 'All B are C', what conclusion necessarily follows?

'All A are C' follows necessarily (also 'Some C are A' and 'Some A are C'). This is the classic transitive Barbara syllogism.

Why can no definite conclusion be drawn from two particular premises (e.g., 'Some A are B' and 'Some B are C')?

Particular premises ('some') do not guarantee any overlap between the end terms; the 'some' groups may be entirely different members, so no valid universal or particular conclusion connecting A and C is forced.

In syllogisms, what is the 'either-or' (complementary pair) rule?

When neither of two conclusions individually follows but together they cover all possibilities (e.g., 'Some A are B' and 'Some A are not B', with the same subject and predicate), the 'either I or O' pair follows.

What is the rule about negative premises in syllogisms?

If even one premise is negative, the conclusion must be negative; and two negative premises yield no valid conclusion. A valid negative conclusion requires exactly one negative premise.

In statement-and-assumption questions, what is the standard test to verify an assumption?

The negation test: negate the proposed assumption; if the argument collapses or becomes meaningless, the assumption is implicit. If the argument still stands, it is not a necessary assumption.

Why are assumptions stating the 'obvious' or 'already established' usually rejected as implicit?

An implicit assumption must be an unstated, taken-for-granted belief necessary to the argument. Statements that are explicitly given, universally obvious, or restate the conclusion are not hidden assumptions the author needed to make.

In a number/letter series, what is the first thing to check to find the pattern?

Check the differences between consecutive terms (and second-order differences); also test for multiplication/division ratios, squares, cubes, primes, or alternating patterns before concluding the rule.

How do you find the missing term in an alphabet sequence such as A, C, F, J, ?

Map letters to positions (A=1, C=3, F=6, J=10) and note the increasing gaps (+2, +3, +4); the next gap is +5, giving position 15 = O.

In coding-decoding logical sequences, what does 'letter-shift' coding mean?

Each letter is replaced by another a fixed number of places forward or backward in the alphabet (e.g., +1 turns CAT into DBU). Identify the constant shift by comparing corresponding letters of word and code.

For passage-based reasoning questions, what should every answer be based on?

Only the information and reasoning contained in the passage itself, not outside knowledge or personal opinion. The correct option is the one the passage best supports or logically entails.

In passage-based reasoning, how do you identify the main point or central argument?

Find the claim that the rest of the passage supports; the main point is what the author is ultimately trying to convince you of, while other sentences serve as evidence, examples, or qualifications.

What does a question asking you to 'strengthen' an argument require you to find?

An option that, if true, makes the conclusion more likely by supporting a premise, confirming the assumption, or ruling out an alternative explanation.

What does a question asking you to 'weaken' an argument require you to find?

An option that, if true, makes the conclusion less likely, typically by attacking the assumption, offering an alternative cause, or providing a counterexample to the reasoning.

When evaluating evidence, what makes a piece of evidence 'relevant' to a conclusion?

Relevant evidence has a logical bearing on the truth of the conclusion, raising or lowering its probability. Irrelevant evidence, however interesting, does not affect whether the conclusion is true.

In evaluating evidence, why is the source's reliability important, and what should you watch for?

Conclusions are only as trustworthy as their evidence; watch for biased sources, small or unrepresentative samples, hearsay, and conflicts of interest, all of which reduce evidentiary weight.

What is the difference between correlation and causation when assessing evidence?

Correlation means two variables move together; causation means one produces the other. Correlation alone may be coincidental, reverse-caused, or due to a third common factor, so it does not prove causation.

What does it mean for a set of statements to be 'logically consistent'?

A set of statements is logically consistent if they can all be true at the same time, that is, no statement contradicts another. If no possible situation makes them all true together, they are inconsistent.

What is a logical contradiction, and how does it differ from contrary statements?

Contradictories cannot both be true and cannot both be false (exactly one holds), e.g., 'All are X' vs 'Some are not X'. Contraries cannot both be true but can both be false, e.g., 'All are X' vs 'No are X'.

In a logic puzzle where exactly one person tells the truth and others lie, what is a reliable solving technique?

Assume each person is the truth-teller in turn, derive the consequences, and keep only the assumption that produces no contradiction among the statements. The consistent case is the solution.

Why does deriving a contradiction from an assumption tell you the assumption is false?

Because a consistent set of true statements cannot entail a contradiction. If assuming something leads to two statements that cannot both be true, the assumption must be rejected (proof by contradiction / reductio ad absurdum).