Question

for all sets A,BandC is A-(B-C)=(A-B)-C?justify your answer
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Answer 1

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FORMULA TO BE IMPLEMENTED

For any two non empty sets A & B

$A - B = \{ \: x : x \in \: A \:, \: x \not\in \: B\: \}$

TO JUSTIFY

We have to justify that does

$A - (B - C ) = (A - B) - C$

ANSWER

NO above equality does not hold

EXPLANATION

Suppose

$A= \{ \: 1,2,3,4 \: \}$

$B = \{ \: 1,2,3\: \}$

$C = \{ \: 1,2 \: \}$

Then

$B - C = \{ \: 3\: \}$

So

$A - (B - C \: ) = \{ \: 1,2,4 \: \}$

Again

$A - B = \{ \: 4 \: \}$

So

$(A - B) - C = \{ \: 4 \: \}$

Clearly

$A - (B - C \: ) \ne(A - B) - C$