Logical Deductions
Logical deduction asks: given a set of premises, what conclusion is forced to be true? The PMDC MDCAT 2026 syllabus expects you to draw conclusions from a passage, evaluate categorical syllogisms using Venn diagrams, and organise premises step-by-step. Expect 1-2 MCQs from this topic in the Logical Reasoning section.
Passage-based Deductions
A passage gives you facts; you must decide what is necessarily true, possibly true, or not supported based only on those facts. The cardinal rule is to stay inside the passage and never import outside knowledge.
Necessarily true vs possibly true
- Necessarily true: The passage forces this conclusion. There is no way the passage can be true while this conclusion is false.
- Possibly true: The passage allows this conclusion but does not force it. It might be true, it might not.
- Not supported / cannot be determined: The passage gives no reason to accept or deny the statement.
Passage: "Every student in Section A scored above 80%. Some students in Section B also scored above 80%."
Necessarily true: "At least one student in Section B scored above 80%." Possibly true: "All students in Section B scored above 80%." Not supported: "Section B has more students than Section A."
If the passage does not mention a fact, you cannot use it — even if you know it personally. The MDCAT examiner is testing logic, not general knowledge.
"All", "some", "no", and "most" each have precise meanings. "Some" means "at least one" — it does not mean "many" or "a few." "All A are B" does not let you conclude "All B are A."
Predicting Relations
A categorical syllogism is an argument with two premises and a conclusion, each in one of four standard forms. The MDCAT favourite is the All/Some pair.
The four standard categorical statements
| Type | Letter | Form | Quantifier | Quality | Venn |
|---|---|---|---|---|---|
| Universal affirmative | A | All A are B | Universal | Affirmative | A circle entirely inside B |
| Universal negative | E | No A are B | Universal | Negative | A and B circles do not overlap |
| Particular affirmative | I | Some A are B | Particular | Affirmative | "X" in the A∩B overlap |
| Particular negative | O | Some A are not B | Particular | Negative | "X" inside A but outside B |
Mnemonic for the letters — from Latin AffIrmo (I affirm) and nEgO (I deny). The vowels mark the four standard forms.
The Venn diagram method
Draw two or three overlapping circles, one for each category. Shade regions that the premises declare empty; place an "X" in regions where they say at least one element exists. Then read off whether the conclusion is forced.
"All A are B; All B are C" forces "All A are C." Draw three nested circles: A inside B inside C.
"All A are B; Some C are A" forces "Some C are B." The element shared between C and A must also be in B because every A is a B.
"Some A are B" + "Some B are C" does not force "Some A are C." The "some" in each statement may refer to different members. This is the most-tested trap.
"No A are B" + "No B are C" tells you nothing about the relationship between A and C. They might overlap, or might not.
"All A are B" does not imply "All B are A." All cats are mammals, but not all mammals are cats. Reversing a universal affirmative is a classic distractor.
| Premise 1 | Premise 2 | Forced conclusion | Notes |
|---|---|---|---|
| All A are B | All B are C | All A are C | Two universals → universal (transitivity) |
| All A are B | No B are C | No A are C | Universal + universal negative |
| All A are B | Some C are A | Some C are B | Universal + particular → particular |
| No A are B | Some C are A | Some C are not B | Universal negative + particular |
| Some A are B | Some B are C | No conclusion | Two particulars give nothing — classic trap |
| No A are B | No B are C | No conclusion | Two negatives give nothing |
| Some A are B | All B are C | Some A are C | Order of "some" doesn't matter |
Worked syllogism
Premise 1: All doctors are graduates. Premise 2: Some graduates are female. Candidate conclusion: Some doctors are female. Does it follow? No. The "some graduates" who are female may not include any of the doctors. By Rule 3, two particular-flavoured premises (after combination) cannot force a particular conclusion across the unshared term.
Structured Thinking
Structured thinking is the discipline of laying out premises step-by-step rather than juggling them in your head. For any deduction question, follow a fixed routine.
The four-step routine
- List the premises exactly as given. Number them P1, P2, P3.
- Translate each premise into a Venn diagram or a simple logical form (e.g., A → B).
- Combine by chaining: if A → B and B → C, then A → C.
- Test each candidate conclusion against the diagram. Pick only the conclusion that the diagram forces.
Premises: "If it rains, the ground is wet." "If the ground is wet, the floor is slippery." Chain: rain → wet → slippery. So "If it rains, the floor is slippery" follows by transitivity.
"If P then Q" is logically equivalent to "If not Q then not P." If "all doctors are graduates", then "anyone who is not a graduate is not a doctor." The contrapositive is always safe; the converse ("All graduates are doctors") is not.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for logical deductions. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. Premise 1: All teachers are educated. Premise 2: Some educated people are wealthy. Which conclusion necessarily follows?
The "some educated people who are wealthy" may include none of the teachers. The two premises do not force any direct relation between teachers and wealth. Always reject conclusions where the middle term ("educated") does not bridge the two extremes.
Q2. Premise 1: All birds have feathers. Premise 2: A sparrow is a bird. Which conclusion follows?
This is a classic universal affirmative + instance: every member of the bird category has feathers, sparrow is a bird, therefore sparrow has feathers. The other options reverse universals or add unsupported claims.
Q3. Premise 1: No reptiles are mammals. Premise 2: All snakes are reptiles. Which conclusion follows?
If the reptile circle and the mammal circle do not overlap (premise 1), and the snake circle sits entirely inside the reptile circle (premise 2), then the snake circle cannot overlap the mammal circle either. So no snakes are mammals.
Q4. "If a student passes the MDCAT, they get admission. Ali got admission." Can we conclude that Ali passed the MDCAT?
The premise says passing the MDCAT is sufficient for admission, not necessary. There may be other routes to admission. Asserting "passed the MDCAT" from "got admission" is the formal fallacy of affirming the consequent.
Q5. Passage: "Every member of the medical society also belongs to the science club. Some science club members do volunteer work." Which is necessarily true?
The "some science club members" who do volunteer work may all lie outside the medical society subset. The passage does not force any link between medical society and volunteer work — classic Rule 3 failure.
Quick Recap
- Use only what the passage gives — never import outside knowledge.
- Necessarily true = forced by premises; possibly true = allowed but not forced.
- Categorical statements: All A are B (A), No A are B (E), Some A are B (I), Some A are not B (O).
- Universal + universal can yield universal; universal + particular yields particular; two particulars yield nothing.
- "All A are B" does not imply "All B are A" — do not reverse universals.
- The contrapositive of "If P then Q" is "If not Q then not P" — always valid.
- Affirming the consequent ("Q happened, so P must have caused it") is invalid.