JEE Mains · Maths · STD 11 - 1. set theory
Let \(A, B\) and \(C\) be sets such that \(\phi \ne A \cap B \subseteq C\). Then which of the following statements is not true ?
- A If \(\left( {A - C} \right) \subseteq B\) then \(A \subseteq B\)
- B If \(\left( {A - B} \right) \subseteq C\) then \(A \subseteq C\)
- C \(\left( {C \cup A} \right) \cap \left( {C \cup B} \right) = C\)
- D \(B \cap C \ne \phi \)
Answer & Solution
Correct Answer
(A) If \(\left( {A - C} \right) \subseteq B\) then \(A \subseteq B\)
Step-by-step Solution
Detailed explanation
For\(A\, = \,C,\,A - C\, = \,\phi \) \( \Rightarrow \phi \, \subseteq \,B\) But\(A\, \subseteq \,B\) \( \Rightarrow \,\) option \(A\) is NOT true Let\(x\, \in \,\,(C\,x\, \in \,(C\, \cup \,A)\,\, \cap (C\, \cup \,B)\,)\) \( \Rightarrow \,x\,(C\, \cup \,A)\) and…
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