For Three Sets A, B and C, Show that a ⊂ B ⇒ C − B ⊂ C − a - Mathematics

Question

For three sets A, B and C, show that \[A \subset B \Rightarrow C - B \subset C - A\]

Solution

\[\text{ Let } z \in C - B . . . (1)\]
\[ \Rightarrow z \in C \text{ and } z \not\in B\]
\[ \Rightarrow z \in C \text{ and } z \not\in A \left[ \because A \subset B \right]\]
\[ \Rightarrow z \in C - A . . . (2)\]
\[\text{ From } (1) \text{ and } (2), \text{ we get }\]
\[C - B \subset C - A\]

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Types of Sets - Universal Set

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Q 6.2 Q 6.1 Q 7.1

Chapter 1: Sets - Exercise 1.06 [Page 27]

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RD Sharma Mathematics [English] Class 11

Chapter 1 Sets
Exercise 1.06 | Q 6.2 | Page 27

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