In the following question, some statements are given followed by some…
2021
In the following question, some statements are given followed by some conclusions based on those statements. Take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow from the given statements.
Statements:
I. Some M are B.
II. No L is M.
Conclusions:
I. No L is B.
II. No M is L.
Answer: B. Only conclusion II follows — Concept A conclusion follows only if it is true in every arrangement of the classes that the statements permit. A single arrangement in which the statements…
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Both conclusions I and II follow
- D.
Neither conclusion follows
Attempted by 155 students.
Show answer & explanation
Correct answer: B
Concept
A conclusion follows only if it is true in every arrangement of the classes that the statements permit. A single arrangement in which the statements hold but the conclusion fails is enough to reject that conclusion.
Simple conversion of a universal negative: 'No X is Y' and 'No Y is X' assert exactly the same exclusion, so each follows immediately from the other.
A particular affirmative, 'Some X are Y', fixes only that X and Y overlap somewhere; it says nothing definite about how Y is related to a third class.
Application
Statement II, 'No L is M', is a universal negative. Converting it simply gives 'No M is L', which therefore holds in every arrangement the statements permit.
For 'No L is B' the statements supply only 'Some M are B' together with L lying wholly outside M. The part of B that falls outside M is left unconstrained.
Arrangement A: draw B wholly inside M. L sits outside M, so L meets no B and 'No L is B' comes out true.
Arrangement B: let B overlap M and also extend outside M into L. Both statements still hold, yet some L is B, so 'No L is B' comes out false.
The truth value of 'No L is B' changes between two arrangements that both satisfy the statements, so it is not entailed.
Cross-check
What the statements do guarantee about B and L is weaker: some M are B, and no L is M, so those particular B's cannot be L. That yields 'Some B are not L', a particular claim. 'No L is B' is a universal claim and asserts far more than the statements support.
Hence Conclusion II ('No M is L') follows from the statements and Conclusion I ('No L is B') does not.