Syllogisms

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

A syllogism is a logical argument consisting of two premises (a major premise and a minor premise) and a conclusion that necessarily follows from them. In CLAT logical reasoning, you must determine whether the conclusion logically follows from the given premises — not whether it is factually true in the real world.

Standard Syllogism Structure:

• Major Premise: A general statement (e.g., “All mammals are warm-blooded”)
• Minor Premise: A specific statement relating to the major term (e.g., “Whales are mammals”)
• Conclusion: The logical deduction (e.g., “Therefore, whales are warm-blooded”)

The Three Terms:

• Major Term (Predicate): Appears in the major premise and the conclusion
• Minor Term (Subject): Appears in the minor premise and the conclusion
• Middle Term: Appears in BOTH premises but NOT in the conclusion (connects the major and minor terms)

In the example above:

• Major term = “warm-blooded” (predicate of the conclusion)
• Minor term = “whales” (subject of the conclusion)
• Middle term = “mammals” (appears in both premises, absent from conclusion)

The Four Quantifiers (Types of Propositions):

Symbol	Quantifier	Meaning	Distribution
A	All	Universal affirmative	Subject distributed; predicate not distributed
E	No	Universal negative	Both subject and predicate distributed
I	Some	Particular affirmative	Neither subject nor predicate distributed
O	Some Not	Particular negative	Predicate distributed; subject not distributed

The Square of Opposition:

Understanding relationships between propositions is key:

    A (All S are P)
   / \
  /   \
 E(No S is P)---I(Some S are P)
  \   /
   \ /
    O (Some S are not P)

• Contradictories (A↔O, E↔I): One must be true, one must be false
• Contraries (A↔E): Both cannot be true at once, but both could be false
• Subcontraries (I↔O): Both cannot be false at once, but both could be true
• Subalternation (A→I, E→O): If A is true, I is true; if I is false, A is false

⚡ Exam Tip (CLAT): The most common error in syllogism questions is confusing what can be “logically concluded” with what is “probably true in real life.” A conclusion follows logically only if it is guaranteed by the premises. If the premises don’t establish it with certainty, it is NOT a valid conclusion. For example, “All cats are mammals. Some cats are black.” You CANNOT conclude “Some black things are cats” from these premises — because although it is true in reality, it is not necessarily guaranteed by the logic given.

⚡ CLAT Trap: Be very careful with the conclusion starting with “Some” vs “All.” From “All S are P,” you CANNOT conclude “Some S are P” — because “all” includes the possibility of “some” (since “all” is a subset of the universal), but in strict logic, a universal statement does not guarantee a particular statement in this direction. However, from “All cats are mammals,” you CAN conclude “Some cats are mammals” only if you accept that the class of cats is not empty. In classical syllogistic logic used in CLAT, we generally assume that when we say “All S are P,” it implies the existence of S, so the subalternation (A→I) does hold.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of logical deduction.

Valid Syllogism Patterns:

There are 24 valid mood combinations (categorical syllogisms). The most important ones for CLAT:

AAA-1 (Barbara):

• All M are P (Major premise)
• All S are M (Minor premise)
• ∴ All S are P (Conclusion)

Example: All humans (M) are mortal (P). All Indians (S) are humans (M). ∴ All Indians (S) are mortal (P).

EAE-1 (Celarent):

• No M are P
• All S are M
• ∴ No S are P

AII-1 (Darii):

• All M are P
• Some S are M
• ∴ Some S are P

EIO-1 (Ferio):

• No M are P
• Some S are M
• ∴ Some S are not P

Testing Validity with Venn Diagrams:

The most reliable method for CLAT syllogisms:

1. Draw three overlapping circles: S (Subject), P (Predicate), M (Middle term)
2. Shade regions that are empty (from universal negative premises — E statements)
3. Place X marks in regions that have at least one member (from particular affirmative — I statements)
4. Check whether the conclusion’s region is necessarily occupied, empty, or undetermined

If-Then (Hypothetical) Syllogisms:

• Affirming the antecedent (Modus Ponens):

  • If P, then Q. (P → Q)
  • P is true.
  • ∴ Q is true. ✓ Valid

• Denying the consequent (Modus Tollens):

  • If P, then Q. (P → Q)
  • Q is false.
  • ∴ P is false. ✓ Valid

• Fallacy: Affirming the consequent:

  • If P, then Q.
  • Q is true.
  • ∴ P is true. ✗ INVALID

• Fallacy: Denying the antecedent:

  • If P, then Q.
  • P is false.
  • ∴ Q is false. ✗ INVALID

⚡ Common CLAT Error: The “affirming the consequent” and “denying the antecedent” fallacies are very common traps in CLAT. Always check whether the argument structure matches a valid form (modus ponens or modus tollens) or an invalid form.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

All 15 Valid Syllogism Forms (by Figure):

The figure of a syllogism is determined by the position of the middle term in the premises:

Figure	Major Premise	Minor Premise
1st	M—P	S—M
2nd	P—M	S—M
3rd	M—P	M—S
4th	P—M	M—S

1st Figure Valid Moods: AAA-1, EAE-1, AII-1, EIO-1, (AAI-1, EAO-1 — weakened)

2nd Figure Valid Moods: AEE-2, EAE-2, AOO-2, EIO-2, (AEO-2, EAO-2 — weakened)

3rd Figure Valid Moods: AII-3, IAI-3, EIO-3, OAO-3, (AAI-3, EAO-3 — weakened)

4th Figure Valid Moods: AEE-4, IAI-4, EIO-4, AEO-4, (AAI-4, EAO-4 — weakened)

(Weakened conclusions use a particular conclusion when a universal could be drawn — they are valid but “weaker.”)

Disjunctive Syllogism:

• P or Q. (P ∨ Q)

• Not P. (¬P)

• ∴ Q. ✓ Valid

• P or Q.

• P.

• ∴ Not Q. ✗ INVALID (unless the “or” is exclusive — which must be specified)

Dilemma:

A dilemma presents two options (both lead to an unwanted conclusion):

• P → R
• Q → R
• P or Q
• ∴ R

Reductio ad Absurdum (Indirect Proof):

To prove that P is false, assume P is true, show that this leads to a contradiction with known truths, therefore P is false.

Conditional Chains:

• If P then Q. (P → Q)
• If Q then R. (Q → R)
• ∴ If P then R. (P → R) ✓ Valid (hypothetical syllogism)

Tips for CLAT Syllogism Questions:

1. Always reduce the argument to its formal structure first
2. Identify which terms are S, P, and M
3. Determine which figure the syllogism is in
4. Check if the mood-figure combination corresponds to a valid form
5. If not automatically valid, use Venn diagrams to test
6. Check for hidden assumptions — the argument may fail because a necessary premise is missing

⚡ Extended Tip — Testing Conclusions: When multiple conclusions are offered:

1. Check each conclusion individually
2. Ask: “Is this conclusion necessarily true given the premises?”
3. If the conclusion could be true OR false depending on information not in the premises, it does NOT follow
4. The correct answer is always the one that is necessarily true, not just possibly true

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