Two statements are given, followed by four conclusions numbered 1, 2, 3 and 4. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows(s) from the statements.
Statements:
All mats are vans.
Some cots are vans.
Conclusions:
All mats are cots.
All cots are mats.
Some vans are cots.
All vans are mats.
- ABoth the conclusions 2 and 3 follow
- BOnly Conclusion 4 follows
- COnly conclusion 3 follows
- DOnly conclusion 1 follows
Solution & Step-by-step Explanation
Let's analyze the conclusions based on the statements:
Statement 2 states: "Some cots are vans." The converse of a particular affirmative statement (Some A are B) is always true (Some B are A). Therefore, "Some vans are cots" definitely follows. This matches Conclusion 3.
No direct definitive relationship is established between 'mats' and 'cots' from the premises, so Conclusions 1 and 2 do not follow.
Statement 1 states: "All mats are vans." Its converse is "Some vans are mats", not "All vans are mats". So Conclusion 4 does not follow.
Thus, only conclusion 3 follows.
Statement 2 states: "Some cots are vans." The converse of a particular affirmative statement (Some A are B) is always true (Some B are A). Therefore, "Some vans are cots" definitely follows. This matches Conclusion 3.
No direct definitive relationship is established between 'mats' and 'cots' from the premises, so Conclusions 1 and 2 do not follow.
Statement 1 states: "All mats are vans." Its converse is "Some vans are mats", not "All vans are mats". So Conclusion 4 does not follow.
Thus, only conclusion 3 follows.