The only part I dont understand is Part C Please show all wo

The only part I dont understand is Part C.

Please show all work, thank you!

6. Can you conclude that A = B if A, B, and C are sets such that Give a counter example or prove your conclusion.

Solution

A,B and C are 3 sets

Given that AUC = BUC

This need not imply A=B

This is proved by the following example.

A = (1,2) C=(1,2,3,4) B = (1,2,3)

Then AUC = BUC here but A not equals B.

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b) A int C = B int C

Let A = (1,2,3,5) B =(1,2,3,4) C = (1,2)

Though A int C = B int C A not equals C

c) With the above examples we get AUC not equals BUC and A int C not equals B int C