Common Syllogistic Patterns

The UCAT Decision Making subtest tends to reuse a relatively small number of syllogistic patterns. Recognising these patterns allows you to solve syllogisms faster and with greater confidence. This lesson catalogues the most common valid and invalid patterns, so you can identify them instantly on test day.

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The Six Most Common Valid Patterns

Pattern 1: Universal Chain (Barbara)

Premise 1	All A are B
Premise 2	All B are C
Conclusion	All A are C

Example:

• All surgeons are doctors.
• All doctors are university graduates.
• Therefore, all surgeons are university graduates. VALID ✓

This is the most intuitive syllogistic pattern. A is inside B, B is inside C, so A is inside C.

Pattern 2: Universal-to-Particular (Darii)

Premise 1	All B are C
Premise 2	Some A are B
Conclusion	Some A are C

Example:

• All pharmacists are science graduates.
• Some hospital staff are pharmacists.
• Therefore, some hospital staff are science graduates. VALID ✓

The "some A" that are in B must also be in C, because all of B is inside C.

Pattern 3: Universal Negative Chain (Celarent)

Premise 1	No B are C
Premise 2	All A are B
Conclusion	No A are C

Example:

• No vegetarians eat meat.
• All vegans are vegetarians.
• Therefore, no vegans eat meat. VALID ✓

A is entirely within B, and B has no overlap with C, so A cannot overlap with C.

Pattern 4: Particular Negative (Ferio)

Premise 1	No B are C
Premise 2	Some A are B
Conclusion	Some A are not C

Example:

• No first-year students are eligible for the advanced module.
• Some biology students are first-year students.
• Therefore, some biology students are not eligible for the advanced module. VALID ✓

The "some A" that are in B cannot be in C (because B and C do not overlap), so at least some A are outside C.

Pattern 5: Contrapositive of Universal Affirmative

Premise	All A are B
Valid conclusion	All non-B are non-A

Example:

• All registered nurses have completed training.
• Therefore, anyone who has not completed training is not a registered nurse. VALID ✓

UCAT Tip: The contrapositive is ALWAYS logically equivalent to the original statement. This comes up frequently — learn to spot it instantly.

Pattern 6: Universal Negative Conversion

Premise	No A are B
Valid conclusion	No B are A

Example:

• No consultants are medical students.
• Therefore, no medical students are consultants. VALID ✓

"No A are B" and "No B are A" are logically equivalent. The order does not matter for universal negatives.

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Recognising Valid Patterns Quickly

Here is a decision table you can use under time pressure:

If you see...	And the conclusion says...	Valid?
All A are B, All B are C	All A are C	✓ Yes
All A are B, All B are C	Some A are C	✓ Yes (if A exists)
All A are B, Some C are A	Some C are B	✓ Yes
No A are B, All C are A	No C are B	✓ Yes
No A are B	No B are A	✓ Yes
All A are B	All non-B are non-A	✓ Yes (contrapositive)

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The Five Most Common Invalid Patterns

Invalid Pattern 1: Affirming the Consequent

Premise 1	All A are B
Premise 2	X is B
Invalid conclusion	Therefore, X is A

Example:

• All surgeons are doctors.
• Dr Patel is a doctor.
• Therefore, Dr Patel is a surgeon. INVALID ✗

Dr Patel could be any type of doctor. Being in B does not guarantee being in A.