Disjunction analysis: “Either CAT is tough or IIT JEE is easy.” Identify the pair of statements that can simultaneously be true without contradicting the given disjunction.

Introduction / Context:We assess truth conditions of a disjunction: “Either CAT is tough or IIT JEE is easy.” In standard logic, “either … or …” is often read exclusively in puzzles, but the safe consistency check works for inclusive-or as well: the disjunction is true if at least one disjunct is true.

Given Data / Assumptions:

• Statement S: (CAT tough) OR (IIT JEE easy).
• Options reference: (ii) CAT is easy; (iii) IIT JEE is easy; (iv) IIT JEE is tough.

Concept / Approach:We must find a pair that does not contradict S. If we pick CAT easy (ii) and IIT JEE easy (iii), S remains satisfied because “IIT JEE easy” makes the disjunction true. Pairs that force both “CAT not tough” and “IIT JEE not easy” would contradict S.

Step-by-Step Solution:

Verification / Alternative check:If we treat “either … or …” as exclusive, (ii)&(iii) still keeps S true (since the clause only requires at least one to make the original sentence consistent; exclusivity is not enforced by the option pair itself).

Why Other Options Are Wrong:

• (ii) and (iv) can force both disjuncts false relative to S (no guarantee CAT is tough).
• (iii) and (iv) is internally inconsistent.
• “None of these” is wrong because (ii)&(iii) is consistent with S.

Common Pitfalls:Assuming “CAT easy” implies “CAT not tough” with certainty. The prompt does not define “tough vs easy” as strict negations; even if treated as opposites, (iii) alone already satisfies S.

Final Answer:(ii) and (iii)