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

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

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Solution

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

Concept: Universal Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.6 | Q 6.2 | Page 27
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