NTS NAT-IGS Analytical Reasoning Syllabus

When should you use a number-line/slot diagram versus a grid/matrix?

Use a slot diagram (positions in a row) for ordering/sequencing; use a grid/matrix for matching or grouping where you cross-reference entities against attributes or groups.

What are common symbols used to diagram analytical reasoning rules?

Arrows (->) for "if...then," blocks (AB) for adjacency, slash (A/B) for alternatives, line-through letters or 'not' bars for negation, and >/< for before/after.

What is logical deduction in analytical reasoning?

The process of deriving new, certain conclusions that must be true by combining the given rules, rather than relying on what is merely possible or assumed.

What is a "valid" deduction?

A conclusion that necessarily follows from the premises; if the premises are true, the conclusion cannot be false.

What is the difference between a deduction that is "must be true" and one that "could be true"?

"Must be true" holds in every valid arrangement allowed by the rules; "could be true" holds in at least one valid arrangement but not necessarily all.

What is a "chain" deduction when combining conditional rules?

Linking rules so the consequent of one feeds the antecedent of the next (A->B and B->C gives A->C), allowing you to deduce far-reaching consequences from a single trigger.

What is an assumption in the context of arguments?

An unstated premise that the argument takes for granted and needs in order for its conclusion to follow logically from its stated premises.

What is a "necessary assumption"?

An assumption the argument must depend on; if it were false, the argument's reasoning would collapse and the conclusion could not be properly drawn.

What is the "negation test" for identifying a necessary assumption?

Negate the candidate assumption; if its negation destroys or seriously weakens the argument, it is a necessary assumption. If the argument survives the negation, it is not necessary.

What is a conclusion in an argument?

The main claim the argument is trying to establish; it is the point supported by the premises (the "therefore" statement).

How can you locate the conclusion of an argument?

Look for indicator words like "therefore, thus, hence, so, consequently," and ask which statement is supported by the others rather than supporting them.

What is the difference between a premise and a conclusion?

A premise is a stated reason offered as evidence; a conclusion is the claim that the premises are meant to support. Premises answer "why?"; the conclusion is "what is claimed."

What does it mean to "strengthen" an argument?

To add information that makes the conclusion more likely to follow from the premises, often by supporting an assumption or ruling out an alternative explanation.

What does it mean to "weaken" an argument?

To add information that makes the conclusion less likely to follow, often by attacking an assumption, offering an alternative explanation, or showing a gap between premises and conclusion.

To weaken a causal argument (X causes Y), what are the classic strategies?

Show an alternative cause for Y, show Y can occur without X, show X can occur without Y, show the cause and effect are reversed, or show the correlation is coincidental.

To strengthen a causal argument (X causes Y), what are the classic strategies?

Rule out alternative causes, show that when X is present Y follows, show that when X is absent Y does not occur, and confirm the direction of causation is X-to-Y.

What is the difference between strengthening/weakening and proving/disproving an argument?

Strengthening/weakening only shifts the likelihood of the conclusion; proving/disproving establishes certainty. Most argument questions ask only to make the conclusion more or less probable.

What is a cause-and-effect statement?

A claim that one event or factor (the cause) produces or brings about another event (the effect).

What is the key reasoning flaw captured by "correlation does not imply causation"?

Two things occurring together (correlated) does not prove one causes the other; the link could be coincidence, reverse causation, or a common third cause.

What is a "confounding" (third) variable in a causal claim?

An outside factor that independently influences both the supposed cause and the supposed effect, creating an apparent causal link where none directly exists.

What is "reverse causation"?

A flaw where the supposed effect is actually the cause; the true direction is Y causes X rather than X causes Y.

What is an if-then (conditional) statement and its standard form?

A statement of the form "If P, then Q" (P -> Q), where P is the antecedent (sufficient condition) and Q is the consequent (necessary condition).

What is the contrapositive of "If P, then Q," and is it logically equivalent?

The contrapositive is "If not Q, then not P" (not Q -> not P). It is always logically equivalent to the original conditional.

What is the converse of "If P, then Q," and is it equivalent to the original?

The converse is "If Q, then P" (Q -> P). It is NOT logically equivalent to the original; assuming it is the "affirming the consequent" error.

What is the inverse of "If P, then Q," and is it equivalent to the original?

The inverse is "If not P, then not Q" (not P -> not Q). It is NOT logically equivalent to the original; assuming it is the "denying the antecedent" error.

What is the valid inference "modus ponens"?

Given "If P then Q" and "P is true," you may validly conclude "Q is true." Affirming the antecedent yields the consequent.

What is the valid inference "modus tollens"?

Given "If P then Q" and "Q is false," you may validly conclude "P is false." Denying the consequent yields denial of the antecedent.

What are the two classic conditional fallacies to avoid?

Affirming the consequent (from P->Q and Q, wrongly concluding P) and denying the antecedent (from P->Q and not P, wrongly concluding not Q). Neither is valid.

In logic, what does the inclusive "OR" mean?

"A or B" is true when at least one of A, B is true, including the case where both are true. It is false only when both A and B are false.

What is the difference between inclusive OR and exclusive OR?

Inclusive OR (default in logic) is true if either or both hold; exclusive OR ("either...but not both") is true only when exactly one holds, false if both or neither hold.

What does logical "AND" require, and how do De Morgan's laws negate AND/OR?

"A and B" is true only when both A and B are true. De Morgan's laws: not(A and B) = (not A) or (not B); not(A or B) = (not A) and (not B).

What is a sufficient condition, and what is a necessary condition?

A sufficient condition guarantees the outcome (if it holds, the result follows). A necessary condition is required for the outcome (without it, the result cannot occur), but does not by itself guarantee it. In P->Q, P is sufficient for Q and Q is necessary for P.