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Properties of Set Operation

Let A=-5, -3,...

Question

Let A={-5, -3, -2, -1}, B={-2, -1, 0} and C={-6, -4, -2}. Find A ( B \ C) and (A \ B) \ C. What can we conclude about set difference operation?

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Solution

$B$ \ $C =$ { $- 1, 0$ }
$\Rightarrow A$ \ $(B$ \ $C) =$ { $- 5, - 3, - 2$ }

$A$ \ $B =$ { $- 5, - 3$ }
$\Rightarrow (A$ \ $B)$ \ $C =$ { $- 5, - 3$ }

We see that $A$ \ $(B$ \ $C) \neq (A$ \ $B)$ \ $C$
Therefore the set difference operator is not associative.

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