NTS NAT-IM Analytical Reasoning Syllabus

In circular arrangements, why does the count of distinct seatings of n people equal (n-1)!?

Because rotations are considered identical; fixing one person removes rotational duplicates, leaving (n-1)! arrangements.

In a two-row seating puzzle where rows face each other, how do you handle "opposite" relationships?

Align the rows so each seat has a fixed partner across; note that a person's left/right is mirrored relative to the person sitting opposite them.

What is the key first deduction to make in any seating puzzle with a "between" clue like "X sits between Y and Z"?

X is flanked by Y and Z (Y and Z are immediate neighbors of X) but the order Y-X-Z vs Z-X-Y may be ambiguous unless another clue fixes it.

What is a matching/assignment game?

A game where each entity is paired with one or more attributes (e.g., person-color, employee-day) and rules constrain which pairings are allowed.

In matching games, what is the difference between a one-to-one and a one-to-many assignment?

One-to-one means each entity gets exactly one attribute and vice versa; one-to-many allows an entity to receive several attributes (or an attribute to be shared).

What grid tool is most effective for matching/assignment problems with two or more variable sets?

A matrix (table) with one variable set as rows and another as columns, marking each cell yes (✓) or no (✗) as rules are applied.

In a matching grid, what deduction follows once a row in a one-to-one match has a confirmed ✓?

Every other cell in that row and that column must be marked ✗, since the entity and attribute are fully used up.

What is a conditional (if-then) statement in logical terms?

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

In "If P then Q," which is the sufficient condition and which is the necessary condition?

P is sufficient (its truth guarantees Q); Q is necessary (it must hold for P to be true). P triggers Q, not the reverse.

What does "P only if Q" translate to in if-then form?

P → Q. "Only if" introduces the necessary condition, so Q is necessary for P.

How do you translate "All A are B" into conditional form?

A → B (if something is an A, then it is a B).

How do you translate "No A are B" into conditional form?

A → not-B (and equivalently B → not-A).

What is the contrapositive of the statement "If P then Q"?

"If not-Q then not-P" (not-Q → not-P). It is logically equivalent to the original and always shares its truth value.

Why is the contrapositive a valid inference but the converse is not?

The contrapositive (not-Q → not-P) is logically equivalent to P → Q, whereas the converse (Q → P) reverses the relationship and does not follow.

What is the converse of "If P then Q," and why is asserting it a fallacy?

The converse is "If Q then P." Asserting it commits the fallacy of affirming the consequent, since Q can be true for reasons other than P.

What is the inverse of "If P then Q," and is it valid?

The inverse is "If not-P then not-Q." It is not a valid inference (it is the contrapositive of the invalid converse) and commits denying the antecedent.

What is "modus ponens"?

A valid form: given P → Q and P is true, conclude Q is true. (Affirming the antecedent.)

What is "modus tollens"?

A valid form: given P → Q and Q is false (not-Q), conclude P is false (not-P). (Denying the consequent.)

How do you build an inference chain from "A → B" and "B → C"?

By hypothetical syllogism, link them into A → C; the contrapositive chain is not-C → not-B → not-A.

When combining the conditionals A → B and not-B → D, what useful chain results?

Take the contrapositive of the first (not-B → not-A) and combine with not-B → D; whenever B is false, both not-A and D follow.

When two conditions overlap, how do you find what is forced?

Apply each rule's trigger, then propagate consequences through every linked conditional (and its contrapositive) until no new deductions appear.

What is the difference between "and" and "or" when combining conditions in a consequent?

"P → (Q and R)" requires both Q and R; "P → (Q or R)" requires at least one of Q or R, so failing both Q and R forces not-P.

In a logic argument, what is the distinction between a "premise" and a "conclusion"?

A premise is a stated reason/evidence offered as support; the conclusion is the claim the premises are meant to establish.

How can you identify the conclusion of an argument?

Look for conclusion indicators (therefore, thus, hence, so, consequently) or ask which statement the others are given to support.

What is a "valid" conclusion in deductive reasoning?

One that must be true if all the premises are true; the conclusion follows with logical necessity, not merely plausibility.

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

"Must be true" holds in every possible arrangement consistent with the premises; "could be true" holds in at least one such arrangement.

What is an assumption in an argument?

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

What is a "necessary assumption" and how do you test for one?

An assumption the argument requires to hold; test it with the negation test: if negating the statement destroys the argument, it is a necessary assumption.

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, typically by attacking an assumption, offering an alternative cause, or showing the evidence does not support the claim.

In cause-and-effect reasoning, what three alternatives can undermine a claim that "A causes B"?

(1) Reverse causation: B actually causes A; (2) a third factor C causes both A and B; (3) the correlation is coincidence. Each weakens the causal claim.