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For all sets ...

Question

For all sets $A, B$ and $C$ , determine whether $A - (B - C) = (A - B) - C$ is true or false. Justify your answer

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Solution

First drawing the Venn diagram for $(B - C)$ and $(A - B)$ followed by Venn diagram of

$A - (B - C)$ and $(A - B) - C$

$∴ A - (B - C) \neq (A - B) - C$

Hence, the statement is false.

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