Prove that set difference is not associative.

we are trying to prove $(A\backslash B)\backslash C \ne A\backslash (B\backslash C)$     M1(A1)

${\text{LHS}} = (A \cap B')\backslash C$     (A1)

$= (A \cap B') \cap C'$     A1

${\text{RHS}} = A\backslash (B \cap C')$

$= A \cap (B \cap C')'$     (A1)

$= A \cap (B' \cup C)$     A1

as LHS does not contain any element of C and RHS does, ${\text{LHS}} \ne {\text{RHS}}$     R1

hence set difference is not associative     AG

Note: Accept answers which use a proof containing a counter example.

Total [7 marks]

This question was found difficult by a large number of candidates, but a number of correct solutions were seen. A number of candidates who understood what was required failed to gain the final reasoning mark. Many candidates seemed to be ill-prepared to deal with this style of question.