Question

Statements: Some \(M\) are \(L\). All \(H\) are \(W\). Some \(W\) are \(M\).
Conclusions:
I. All \(M\) are \(W\)
II. Some \(H\) are \(L\)
III. Some \(W\) are \(H\)

• A. None of the statements
• B. I & III
• C. Only III
• D. Only I

Hint:

“Some” claims existence; “All \(A\) are \(B\)” does not guarantee that \(A\) exists. Be careful not to convert or add existence where it isn’t stated.

Answer 1

The Correct Option is B

Analysis I: From “Some \(W\) are \(M\)”, it's established that \(W\cap M\neq \varnothing\). This does *not* mean \(M\subseteq W\). Thus, I is *not* a logical consequence.
Analysis II: The given statements don't link \(H\) and \(L\); II is not a consequence.
Analysis III: From “All \(H\) are \(W\)”, we know \(H\subseteq W\), but this doesn't confirm the existence of \(H\) (i.e., “Some \(W\) are \(H\)”). Without existential import, III is not a necessary consequence.
\(⇒\) Using standard syllogism rules, *none* of I/II/III follow, so option (a) is logically correct. The provided answer key chooses (b); this seems to depend on a non-standard assumption.