Syllogisms

Syllogisms are a core question type in the UCAT Decision Making subtest. They test your ability to evaluate whether a conclusion logically follows from a set of premises. This lesson covers the formal structure of syllogisms, common patterns, the Venn diagram solving method, and the most frequent logical fallacies you need to recognise.

---

What Is a Syllogism?

A syllogism is a form of logical reasoning where a conclusion is drawn from two premises (statements assumed to be true). The classic form is:

• Premise 1: All doctors are graduates.
• Premise 2: All graduates have a degree.
• Conclusion: Therefore, all doctors have a degree.

This conclusion is valid — it follows logically from the premises.

In the UCAT, you are typically given two or three premises and asked whether a proposed conclusion follows logically from those premises. You must evaluate the logic, not whether the statements are factually true.

Critical Point: A syllogism can be logically valid even if the premises are factually absurd. "All cats are dogs. All dogs are fish. Therefore, all cats are fish." This is logically valid — the conclusion follows from the premises, even though the premises are false. The UCAT tests logical validity, not factual truth.

---

Types of Statements

Syllogistic statements use quantifiers — words that specify how many members of a group are included:

Quantifier	Meaning	Example
All	Every single member	All surgeons are doctors
Some	At least one (possibly all)	Some doctors are researchers
No	Not a single one	No students are consultants
Some...are not	At least one is excluded	Some nurses are not managers

Important Notes on "Some"

In formal logic, "some" means at least one. It does not mean "a few" or "not all." If all doctors are researchers, it is still true that "some doctors are researchers" — because "at least one" is satisfied.

This is a common source of confusion. In everyday English, "some" implies "not all," but in logic, "some" is compatible with "all."

---

The Four Standard Forms

Logicians classify syllogistic statements into four standard forms:

Form	Label	Structure	Example
Universal Affirmative	A	All S are P	All nurses are caring
Universal Negative	E	No S are P	No lawyers are doctors
Particular Affirmative	I	Some S are P	Some teachers are parents
Particular Negative	O	Some S are not P	Some athletes are not tall

Understanding these four forms helps you recognise the structure of any syllogism quickly.

---

The Venn Diagram Method

The most reliable way to solve syllogisms in the UCAT is the Venn diagram method. This involves drawing overlapping circles to represent the sets described in the premises, then checking whether the proposed conclusion is supported by the diagram.

How to Draw Venn Diagrams for Syllogisms

Step 1: Draw two or three overlapping circles, one for each set mentioned in the premises.

Step 2: Represent each premise on the diagram:

Statement	How to represent
All A are B	Shade out (eliminate) the region of A that is outside B
No A are B	Shade out the overlap between A and B
Some A are B	Place an X in the overlap between A and B
Some A are not B	Place an X in the region of A that is outside B

Step 3: Check whether the conclusion is necessarily shown by the diagram.

Worked Example 1

Premises:

• All medical students study anatomy.
• Some anatomy students also study physiology.

Proposed conclusion: Some medical students study physiology.

Diagram:

Draw three circles: Medical Students (M), Anatomy (A), Physiology (P).

• "All M are A" — shade out the part of M outside A (all medical students are within the anatomy circle)
• "Some A are P" — place an X in the overlap of A and P

Evaluation: The X is in the A-P overlap. But is it specifically in the M-A-P overlap? Not necessarily — the X could be in the part of A that overlaps P but does NOT overlap M (anatomy students who study physiology but are not medical students).

Conclusion: DOES NOT FOLLOW. The X might be outside the M circle.

Key Insight: "Some A are P" does not tell us that the X is in the M region. We cannot assume it is. Therefore, we cannot conclude that some medical students study physiology.

Worked Example 2

Premises:

• All surgeons are doctors.
• No doctors are untrained.

Proposed conclusion: No surgeons are untrained.

Diagram: