Question

Two statements are given followed by four conclusions J, K, L, M taking statements to be true even if they are at variance from the commonly known facts. Decide which conclusion logically follows from the given statement.
Statement:
Some bottles are drinks.
All drinks are cups.
Conclusions:
(J) Some bottles are cups
(K) Some cups are drinks
(L) All drinks are bottles
(M) All cups are drinks

• A. Only J and K follow.
• B. Only K and L follow.
• C. Only K and M follow.
• D. Only L and M follow.

Hint:

Remember the standard conversion rules for syllogisms:
- "All A are B" converts to "Some B are A"
- "Some A are B" converts to "Some B are A"
This makes evaluating immediate inferences like Conclusion K instant.

Answer 1

The Correct Option is A

Step 1: Restate what is given.
Premise 1 is an I-type statement, $\text{Some bottles are drinks}$, and Premise 2 is an A-type statement, $\text{All drinks are cups}$. Let us picture this with overlapping regions.
Step 2: Draw the smallest valid diagram.
Place the circle for drinks fully inside the circle for cups, since all drinks are cups. Then let the bottles circle overlap the drinks region in at least one shared part.
Step 3: Test conclusion J, some bottles are cups.
The shaded overlap of bottles and drinks sits inside cups, so that shaded part is also bottles-and-cups. Hence $\text{Some bottles are cups}$ is forced true. J follows.
Step 4: Test conclusion K, some cups are drinks.
From $\text{All drinks are cups}$, the immediate inference (conversion of an A statement) is $\text{Some cups are drinks}$. This is always valid. K follows.
Step 5: Reject L and M.
L says all drinks are bottles, but we only know some overlap, so the rest of drinks may lie outside bottles. M says all cups are drinks, which reverses the A statement wrongly. Both fail.
Step 6: Combine.
Only J and K are compelled by the premises.
\[ \boxed{\text{Only J and K follow.}} \]