Introduction / Context:
This is a standard syllogism (logical deduction) question. We are given three categorical statements about sets (tigers, lions, cows, camels) and asked which of the listed conclusions must be true. The task is to reason strictly from the given statements without importing external facts.
Given Data / Assumptions:
- All tigers are lions (T ⊆ L).
- No cow is a lion (Cows ∩ L = ∅).
- Some camels are cows (∃ Camels ∩ Cows).
- We consider only necessary conclusions (must be true in every valid Venn arrangement consistent with the statements).
Concept / Approach:
- If A ⊆ B and B is disjoint from C, then A is also disjoint from C.
- “Some X are Y” asserts existence of overlap; “No X is Y” asserts total disjointness.
- Test each conclusion by constructing or imagining Venn diagrams consistent with the premises.
Step-by-Step Solution:
From “Some camels are cows” and “No cow is a lion,” those particular camels are not lions.Since all tigers are lions, anything that is a tiger must be a lion. Therefore, anything not a lion cannot be a tiger.Thus, the camels that are cows (and hence non-lions) cannot be tigers. So Conclusion II (“No camel is a tiger”) follows.Conclusion I (“Some lions are camels”) is impossible because the camels we know about are cows, and cows have empty intersection with lions.Conclusion III (“Some tigers are cows”) is impossible because tigers are lions while cows are not lions, so their intersection is empty.
Verification / Alternative check:
Sketching a Venn diagram with L containing T entirely, and C disjoint from L, then placing some Camels overlapping C (outside L) confirms II and refutes I and III.
Why Other Options Are Wrong:
“Only I”, “Only III”, “Either I or II”, and “None” contradict the necessity just shown.
Common Pitfalls:
Assuming “some camels are cows” implies anything about camels and lions directly; always route through the disjointness and subset relations first.
Final Answer:
Only II follows
Discussion & Comments