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: Understanding the Question:
We need to analyze the two given premises using syllogistic reasoning to determine which of the four conclusions logically follow.

Step 2: Detailed Explanation:
Let us evaluate each conclusion using rules of deduction or Venn diagrams:
- Premise 1: "Some bottles are drinks." (I-type proposition: \( \text{Some } B \text{ are } D \))
- Premise 2: "All drinks are cups." (A-type proposition: \( \text{All } D \text{ are } C \))
Now, let us test each conclusion:
1. Conclusion (J): Some bottles are cups.
From Premise 1, we know there is an intersection between "bottles" and "drinks". Since all "drinks" are inside "cups" (Premise 2), the part of "bottles" that is "drinks" must also be inside "cups". Hence, "Some bottles are cups" is a valid conclusion. (J follows)
2. Conclusion (K): Some cups are drinks.
Premise 2 states "All drinks are cups". In syllogisms, the converse of "All A are B" is always "Some B are A". Thus, "Some cups are drinks" is a valid conclusion. (K follows)
3. Conclusion (L): All drinks are bottles.
We are only given "Some bottles are drinks". We cannot generalize that all drinks are bottles. Thus, this is invalid. (L does not follow)
4. Conclusion (M): All cups are drinks.
From "All drinks are cups", we cannot conclude "All cups are drinks" (which is an improper converse). Thus, this is invalid. (M does not follow)
Therefore, only conclusions J and K logically follow.

Step 3: Final Answer:
(A) Only J and K follow.