Conclusions
Test whether conclusions follow from premises.
Conclusions
Testing Conclusions from Premises
What you'll learn
- To decide whether a conclusion necessarily follows from given premises (statements).
- Difference between definitely true, possibly true, and definitely false conclusions.
- A checking routine: diagram → test each conclusion → reject extras.
- Core syllogism skill for Class 5 reasoning papers.
NCERT / CBSE link
CBSE Class 5 reasoning and Math-Magic 5, Chapter 7 (Can You See the Pattern?) train "what must follow from a rule" — the same logic as testing conclusions.
Key concepts
Level 1 — Follow vs does not follow
Verbal: Conclusion follows only if it must be true whenever premises are true — no extra assumptions.
Symbolic: Premise 1 + Premise 2 ⊢ Conclusion? (yes/no)
| Premises | Conclusion | Follows? |
|---|---|---|
| All A are B; All B are C | All A are C | Yes |
| All A are B | All B are A | No |
| Some A are B | All A are B | No |
| No A are B | Some A are B | No |
Method: 1) Draw Venn. 2) Read conclusion. 3) Ask "Could picture break this?"
Level 2 — Two-premise puzzles
Verbal: Order of premises does not matter — combine information.
Real-life: If all mammals breathe air, and all dogs are mammals → all dogs breathe air.
| Trap conclusion | Why wrong |
|---|---|
| Some C are A | From All A are C only — C may have non-A |
| No conclusion | Sometimes premises unrelated |
Worked example
Premises: (1) All parrots are birds. (2) Some birds are green. Conclusion: Some parrots are green. Follows?
Step 1 — Parrots inside birds; some birds green — green birds may be outside parrot circle.
Step 2 — Parrots might all be non-green.
Answer: Does **not** necessarily follow.
Premises: (1) All squares are rectangles. (2) All rectangles are quadrilaterals. Conclusion: All squares are quadrilaterals.
Step 1 — Chain: squares ⊆ rectangles ⊆ quadrilaterals.
Answer: **Follows** — must be true.
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Assume what "sounds right" | Real-world bias | Logic only from given lines |
| Some → All jump | Overgeneralise | Need proof for all |
| Ignore possibility of empty set | Edge case | If no A exist, some conclusions vacuous (intro) |
| One diagram fits, skip second conclusion | Partial check | Test each conclusion separately |
Quick check
- All A are B; All B are C. All A are C?
- Some A are B. All A are B?
- No A are B. No B are A?
- Stretch: All cats are mammals. No mammals are plants. Conclusion about cats and plants?
Revision tip: Write "MUST BE TRUE" or "NOT SURE" next to each conclusion before looking at options — slows guessing.
Open the Practice tab for graded questions on Testing Conclusions.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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