COMSATS NTS-based Test Analytical Reasoning Syllabus

In syllogisms, what rule governs negative premises and the conclusion?

If either premise is negative, the conclusion must be negative; and two negative premises yield no valid conclusion.

What is the 'middle term' in a syllogism and what must it do for validity?

The middle term is the term common to both premises but absent from the conclusion; it must be 'distributed' (refer to all members) at least once for the syllogism to be valid.

What is an 'assumption' in the context of 'statement and assumption' questions?

An assumption is something taken for granted — an unstated premise that the speaker/author must believe to be true for the statement to make sense or hold.

How do you test whether something is a necessary assumption of an argument?

Use the negation test: negate the candidate assumption; if the argument falls apart or becomes illogical, it is a necessary assumption. If the argument still holds, it is not assumed.

What distinguishes a valid 'conclusion' from a mere restatement in statement-conclusion questions?

A valid conclusion is a new judgment that logically follows from and goes beyond the given statement(s); a restatement merely repeats given information and is not a true conclusion.

In 'cause and effect' questions, what defines the cause and the effect?

The cause is the event/factor that occurs first and produces a result; the effect is the outcome that follows from and is produced by the cause.

What is the key warning when inferring cause and effect from correlation?

Correlation does not imply causation — two events occurring together may share a common cause or be coincidental; reversed causation or a third (confounding) factor must be ruled out.

In cause-effect reasoning, what is a 'common cause' situation?

When two observed effects are both produced by a single underlying cause, so neither effect causes the other even though they correlate (e.g., heat causing both ice-cream sales and sunburn).

What does it mean to 'strengthen' an argument?

To add information that makes the argument's conclusion more likely or better supported — closing gaps, supporting the assumption, or providing confirming evidence.

What does it mean to 'weaken' an argument?

To add information that makes the conclusion less likely — attacking an assumption, offering an alternative explanation, or providing counter-evidence to the reasoning.

Which has the bigger effect on an argument: attacking its premises or attacking its assumption?

Attacking a hidden necessary assumption is usually the most powerful way to weaken, because the argument depends on that unstated link; undermining it collapses the inference even if stated premises are true.

In strengthen/weaken questions, why is an answer that is 'out of scope' incorrect?

Because it does not bear on the specific gap between the stated evidence and conclusion; only information directly affecting that logical link strengthens or weakens the argument.

What is the standard structure of an 'If-Then' (conditional) statement?

'If P, then Q', where P is the antecedent (hypothesis/sufficient condition) and Q is the consequent (conclusion/necessary condition); it asserts that whenever P holds, Q holds.

For the conditional 'If P then Q', which inference is valid: affirming the antecedent or affirming the consequent?

Affirming the antecedent (modus ponens: P is true, therefore Q) is valid. Affirming the consequent (Q is true, therefore P) is a FALLACY.

State modus ponens and modus tollens for 'If P then Q'.

Modus ponens: P is true ⟹ Q is true. Modus tollens: Q is false (not-Q) ⟹ P is false (not-P). Both are valid forms of inference.

Why is 'denying the antecedent' a logical fallacy?

From 'If P then Q', knowing not-P does NOT let you conclude not-Q, because Q could be caused by something other than P. So 'not P, therefore not Q' is invalid.

In conditional logic, what is a 'necessary condition'?

A condition that must be present for an outcome to occur; without it, the outcome cannot happen. In 'If P then Q', Q is necessary for P (P cannot occur without Q).

In conditional logic, what is a 'sufficient condition'?

A condition whose presence guarantees the outcome. In 'If P then Q', P is sufficient for Q — having P is enough to ensure Q (though Q may also arise otherwise).

How do you distinguish 'P is sufficient for Q' from 'P is necessary for Q' using arrow notation?

'P is sufficient for Q' = P → Q. 'P is necessary for Q' = Q → P (i.e., Q cannot happen without P). The arrow points from the sufficient condition to the necessary one.

When is a condition both necessary AND sufficient, and how is it written?

When each implies the other: P → Q and Q → P, written as P ↔ Q ('P if and only if Q'). P and Q always hold together or fail together.

What is the negation of the statement 'All cats are black'?

'At least one cat is not black' (i.e., 'Some cats are not black'). The negation of a universal affirmative (A) is a particular negative (O).

What is the negation of 'Some students passed'?

'No student passed' (i.e., 'All students did not pass'). The negation of a particular affirmative (I) is a universal negative (E).

How do you negate a conditional statement 'If P then Q'?

The negation is 'P and not Q' (P is true while Q is false) — that is the only case making the conditional false. Negation is NOT 'If P then not Q'.

What is the contrapositive of 'If P then Q', and what is its logical status?

The contrapositive is 'If not Q then not P' (¬Q → ¬P). It is logically EQUIVALENT to the original conditional — always has the same truth value.

Distinguish the converse, inverse, and contrapositive of 'If P then Q'.

Converse: 'If Q then P' (Q→P). Inverse: 'If not P then not Q' (¬P→¬Q). Contrapositive: 'If not Q then not P' (¬Q→¬P). Only the contrapositive is equivalent to the original; converse and inverse are equivalent to each other but not to the original.

In letter coding, if in a code 'CAT' is written as 'DBU', what coding rule is used?

Each letter is shifted forward by one position in the alphabet (C→D, A→B, T→U). This is a forward letter-shift (+1) substitution code.

What is the standard place value of letters used in number coding, forward and backward (EJOTY trick)?

Forward: A=1, B=2 … Z=26. Backward: A=26, B=25 … Z=1. The EJOTY mnemonic gives quick checkpoints: E=5, J=10, O=15, T=20, Y=25.

In substitution coding, if 'milk' is called 'water', 'water' is called 'air', what do you drink when thirsty?

You drink 'air' — because the real water has been renamed 'air' in the code. Always answer using the substituted name for the real-world item asked about.

In a number/series, what is the next term: 2, 6, 12, 20, 30, __ ?

42. The differences are 4, 6, 8, 10, 12 (increasing even numbers), so 30 + 12 = 42. (Equivalently n(n+1): 2,6,12,20,30,42.)

In pattern recognition, what are the common rule types to check when finding the next term of a series?

Check for: arithmetic (constant difference), geometric (constant ratio), squares/cubes, prime numbers, alternating series, difference-of-differences (second-order), and combined/multiplicative patterns.