For three sets *A*, *B* 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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