OnlineCBT
Mathematics · JEE I SETS
हिन्दीGiven below are four statements for any three sets \( A, B, \) and \( C \): (A) If \( A \in B \) and \( B \subset C \), then \( A \subset C \). (B) If \( A \subset B \) and \( B \in C \), then \( A \in C \). (C) If \( A \subset B \) and \( B \subset C \), then \( A \subset C \). (D) If \( A \not\subset B \) and \( B \not\subset C \), then \( A \not\subset C \). Choose the correct statement(s) from the options given below:
View Answer & Solution
Correct answer · Option C
(C) only
Explanation
Subset inclusion is transitive: \( A \subset B \) and \( B \subset C \implies A \subset C \) (C is correct). The other three are false: for (A), \( A \in C \) holds, not \( A \subset C \); for (D), \( A = \{1\}, B = \{2\}, C = \{1, 3\} \) gives a counterexample.
