DM: Syllogisms & Logical Deduction

What Are Syllogisms?

A syllogism is a logical argument consisting of two premises and a conclusion. In the UCAT, you are given premises and asked whether a particular conclusion necessarily follows. The key word is necessarily — the conclusion must be guaranteed by the premises, not merely possible.

Standard Syllogism Structure

Premise 1: All A are B.
Premise 2: All B are C.
Conclusion: Therefore, all A are C. → Valid

Types of Statements

• Universal Affirmative (All A are B): Every member of group A is also a member of group B
• Universal Negative (No A are B): No member of group A is a member of group B
• Particular Affirmative (Some A are B): At least one member of group A is also a member of group B
• Particular Negative (Some A are not B): At least one member of group A is not a member of group B

Common Valid Forms

1. All A are B + All B are C → All A are C ✓
2. All A are B + No B are C → No A are C ✓
3. Some A are B + All B are C → Some A are C ✓
4. All A are B + Some B are C → INVALID (we cannot conclude ‘Some A are C’ because the ‘some B that are C’ might not overlap with A)

Common Invalid Forms (Traps!)

1. Affirming the consequent: All A are B + X is B → X is A (INVALID — B could include non-A members)
2. Denying the antecedent: All A are B + X is not A → X is not B (INVALID — X could still be B via another route)
3. Undistributed middle: All A are B + All C are B → All A are C (INVALID — A and C are both subsets of B but may not overlap)

The Venn Diagram Method

For complex syllogisms, draw Venn diagrams:

1. Draw a circle for each term (A, B, C)
2. Shade or mark regions based on the premises
3. Check if the conclusion is necessarily true based on your diagram
4. If you can draw a diagram where the premises are true but the conclusion is false, the conclusion does NOT follow

UCAT-Specific Syllogism Tips

• Pay extreme attention to the quantifiers: ‘all’, ‘some’, ‘no’, ‘none’ — these change everything
• ‘Some’ means ‘at least one’ in logic, not ‘a few’ or ‘many’
• Watch for the word ‘only’: “Only doctors can prescribe” means “If someone can prescribe, they are a doctor” — NOT “All doctors prescribe”
• If a conclusion uses a stronger quantifier than the premises support, it is invalid