Using properties of sets prove the statements given:-

(i) For all sets A and B, AU(B-A) = AUB

(ii) For all sets A and B, A-(A-B) = AintersectionB

(iii) For all sets A and B, (AUB)-B = A-B

To show that A u (B - A) = A U B we need to show two things: 
1) A U (B - A)  A U B. 
2) A U B  A U (B - A) 

First, let x A U (B - A). 
xA or xB-Aor  xAB or  xB and xAor  xAB or  xBThus xABSo AB-AAB.......1Now let xAB
xA or xB and xAxA or xB-AxAB-ASo ABAB-A......2Now using equation 1 and 2, AB=AB-AHence proved.

In the similar way should try for the other two for your own practice.

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