Show that if A ⊂ B, then C – B ⊂ C – A.

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Solution

The sets are given as,

A⊂B

Assume x is an element of set C but not of set B, that is,

x∈C−B(1)

A is the subset of B, therefore,

x∈C−A(2)

From conditions (1) and (2),

An element belongs to set C − Band also belongs to set C − A.

Hence,

C−B⊂C−A

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