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) X and Y are siblings.
(ii) X and Y do not quarrel.
(iii) Siblings are known to quarrel often.
(iv) X and Y quarrel often.
(v) All those who quarrel are siblings.
(vi) X and Y cannot be siblings.

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

Hint:

Find the general rule about siblings, then the statement that puts X and Y inside that class. The third statement should be the rule applied to them.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A logically related set means two of the three statements act as premises and the third follows from them as a conclusion. The task is to find the option whose three statements form such a valid chain.

Step 2: Key Formula or Approach:
Use the standard categorical form. If every member of a class has a property, and a given item belongs to that class, then the item has the property. In symbols, All A are B and X is an A, so X is a B. Any set that fits this pattern is valid.

Step 3: Detailed Explanation:
Check option (C), which is i, iii, iv.
Premise (iii): siblings are known to quarrel often, so quarrelling often is a property of the class of siblings.
Premise (i): X and Y are siblings, so X and Y belong to that class.
Conclusion (iv): X and Y quarrel often. That is the class property applied to a member of the class, so the chain is valid.

Step 4: Testing the other options:
Option (A) is ii, iv, v. Statements (ii) and (iv) contradict each other, since one says X and Y do not quarrel and the other says they quarrel often. A set holding a direct contradiction cannot form a valid chain.
Option (B) is i, iv, vi. Statement (i) says X and Y are siblings and (vi) says they cannot be siblings, another straight contradiction, and (iv) does nothing to link them.
Option (D) is i, ii, v. From (v) all those who quarrel are siblings, and from (ii) X and Y do not quarrel, no conclusion about their being siblings follows. Denying the property of a class tells you nothing about class membership, since the rule runs from quarrelling to sibling and not the other way. Statement (i) therefore does not follow, and this is the fallacy of denying the antecedent.

Step 5: Final Answer:
Only i, iii, iv forms a valid chain, so the answer is option (C).