UPSC NDA 2 2019 Mathematics Solved Paper

Concept:The question tests knowledge of basic set identities: absorption laws and distributive laws for union and intersection.Explanation:Let us verify each option using known set relations.For option A: $A \cup (A \cap B)$. By the absorption law, $A \cup (A \cap B) = A$. But the option claims it equals $A \cup B$, which is not true in general. For example, if $A = \{1,2\}$, $B = \{2,3\}$, then $A \cup (A \cap B) = \{1,2\}$, while $A \cup B = \{1,2,3\}$. Thus option A is incorrect.For option B: $A \cap (A \cup B)$. By absorption, $A \cap (A \cup B) = A$. This matches the option, so it is correct.For option C: $(A \cap B) \cup C$. By distributive law, $(A \cap B) \cup C = (A \cup C) \cap (B \cup C)$. This matches the option, so it is correct.For option D: $(A \cup B) \cap C$. By distributive law, $(A \cup B) \cap C = (A \cap C) \cup (B \cap C)$. This matches the option, so it is correct.Therefore, only option A is not a correct relation.Answer:Option A: $A \cup (A \cap B) = A \cup B$ is not correct.