Question

The question contains six statements followed by four sets of combination of three. Choose the set in which the statements are logically related.

Statements:
(i) All mangoes are fruits.
(ii) All mangoes are green.
(iii) All mangoes are oval shaped.
(iv) All fruits are sweet.
(v) All mangoes are sweet.
(vi) All fruits are expensive.

• A. i, ii, iii
• B. i, iv, v
• C. ii, iii, iv
• D. iv, v, vi

Hint:

Look for two statements sharing one common class that links them, then see which statement is the result of that chain with the common class removed.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need the set of three where two statements serve as premises and the third is a conclusion drawn from them. All six statements here are universal affirmatives of the form All A are B, so the syllogism rules apply cleanly.

Step 2: Key Formula or Approach:
The rule to use is the chain rule for universals. If All A are B and All B are C, then All A are C. The two premises must share one common term, called the middle term, which drops out of the conclusion.

Step 3: Detailed Explanation:
Check option (B), which is i, iv, v.
Premise (i): All mangoes are fruits, so the class of mangoes sits inside the class of fruits.
Premise (iv): All fruits are sweet, so the class of fruits sits inside the class of sweet things.
The middle term is fruits, and it links the two premises. Since mangoes are inside fruits and fruits are inside sweet things, mangoes are inside sweet things.
Conclusion (v): All mangoes are sweet. The chain is valid, and note that the middle term fruits has vanished from the conclusion, exactly as it should.

Step 4: Testing the other options:
Option (A) is i, ii, iii. All three have mangoes as the subject and give three unrelated properties, fruits, green and oval shaped. There is no shared middle term to chain, so no statement follows from the other two.
Option (C) is ii, iii, iv. Statements (ii) and (iii) are about mangoes being green and oval, while (iv) is about fruits being sweet. Nothing connects greenness or oval shape to sweetness, so no conclusion emerges.
Option (D) is iv, v, vi. Here (iv) says all fruits are sweet and (vi) says all fruits are expensive. Both share fruits as the subject, not as a linking middle term, so at best you get some sweet things are expensive. That does not give (v), all mangoes are sweet, because mangoes never enter the premises at all.

Step 5: Final Answer:
The valid chain is i, iv, v, so the answer is option (B).