Critical Reasoning

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your HAT-UG exam.

What is Critical Reasoning? Critical reasoning is the skill of evaluating arguments — identifying what is claimed, what evidence supports it, and whether the logic is sound. HAT-UG tests your ability to analyse, evaluate, and apply information presented in written form.

Anatomy of an Argument:

Every argument has:

• Conclusion: The main claim the author is trying to establish
• Premises: Evidence or reasons offered to support the conclusion
• Hidden assumptions: Unstated beliefs that link premises to conclusion

How to Find the Conclusion: Ask: “What is the author trying to convince me of?” The conclusion is usually signalled by words like: therefore, thus, hence, so, consequently, it follows that, this shows that, this suggests that.

How to Find the Premises: Premises are typically signalled by: because, since, for, given that, as shown by, for example, the reason is.

⚡ HAT-UG Tip: When asked “Which of the following is the main conclusion?” look for the statement that all other statements support. When asked “Which statement best expresses the author’s overall point?” you are being asked for the conclusion.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for HAT-UG Analytical Reasoning students with a few days to months.

Question Types on HAT-UG:

1. Strengthen/Weaken Questions:

• “Which of the following, if true, would most strengthen the argument?”
• “Which of the following, if true, would most weaken the argument?”

To strengthen: Add evidence that supports the conclusion or eliminates an alternative explanation. To weaken: Add evidence that undermines the conclusion or reveals a flaw in the logic.

2. Assumption Questions:

• “The argument assumes which of the following?”
• An assumption is a hidden premise — something that must be true for the argument to work.

3. Inference Questions:

• “It can be inferred from the passage that…”
• The answer is not stated directly but must be true if all premises are true.

4. Parallel Reasoning:

• “Which of the following has the same logical structure as the argument above?”

5. Evaluating Evidence:

• “Which of the following best describes the kind of evidence used in the argument?”

Common Logical Fallacies:

Fallacy	Description	Example
Ad hominem	Attacking the person, not the argument	”You’re wrong because you’re not a doctor”
Straw man	Misrepresenting the opponent’s argument to attack it	”I think we should have better roads” → “You want to destroy all highways”
False dilemma	Presenting only two options when more exist	”You’re either with us or against us”
Hasty generalisation	Drawing a broad conclusion from limited evidence	”I met two rude people from Lahore, so all Lahoris are rude”
Circular reasoning	The conclusion is restated as a premise	”The Bible is true because it says so in the Bible”
Appeal to authority	Citing an expert in an unrelated field	”A famous athlete says this diet is best, so it must be”
Post hoc	Assuming cause because one event followed another	”It rained after I washed my car, so washing caused rain”

⚡ HAT-UG Common Mistakes:

• Confusing a premise with the conclusion
• Choosing an answer that strengthens/weakens a minor point rather than the main argument
• Mixing up correlation and causation

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for HAT-UG and competitive exams requiring critical reasoning.

Formal Logic:

Conditional statements: If P, then Q.

• P → Q (P implies Q)
• If the antecedent (P) is true, the consequent (Q) must be true.
• If Q is false, then P must be false (modus tollens).
• P can be true with Q true; P can be false with Q true or false.

Biconditional: P if and only if Q (P ↔ Q) means both P → Q and Q → P must hold.

Negation:

• ¬P means “not P”
• ¬(P and Q) = ¬P or ¬Q (De Morgan’s Law)
• ¬(P or Q) = ¬P and ¬Q (De Morgan’s Law)

Disjunction:

• P or Q is true if at least one is true (inclusive “or”)
• P or Q is false only when both are false (exclusive “or” differs)

Arguments Forms:

Modus ponens (affirming antecedent): If P → Q. P is true. ∴ Q is true. VALID.

Modus tollens (denying consequent): If P → Q. Q is false. ∴ P is false. VALID.

Affirming the consequent: If P → Q. Q is true. ∴ P is true. INVALID (post hoc ergo propter hoc fallacy).

Denying the antecedent: If P → Q. P is false. ∴ Q is false. INVALID.

Sufficient and Necessary Conditions:

• P is a sufficient condition for Q: If P, then Q (P → Q)
• P is a necessary condition for Q: If not P, then not Q (¬P → ¬Q), equivalently Q → P
• If P is both sufficient and necessary: P ↔ Q

Analytical Reasoning — Logic Games:

In multi-conditional reasoning sets:

1. List all given conditions clearly
2. Identify what must be true, what could be true, and what cannot be true
3. Combine conditions to find chains (A → B, B → C, so A → C)
4. Look for contrapositives (if P → Q, then ¬Q → ¬P)

Inference with Conditionals: From P → Q, you can infer:

• If Q is false, P must be false (modus tollens)
• If P is true, Q could be true but not necessarily (you cannot affirm Q)

⚡ HAT-UG Patterns:

• HAT-UG has a dedicated analytical reasoning/logic section
• Questions involve conditional reasoning, assumptions, strengthening, and weakening arguments
• Practice with LSAT-style critical reasoning questions for the best preparation

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