Wednesday, February 10, 2010

Determine if the statement is true or false and prove it. For all sets A, B,and C, A-(B-C) = (A-B)-C.?

I am VERY new to discrete mathematics and am having a really hard time with this. Need help with this question in the steps and how to prove it. Thanks! Its on Set Theory.





If the statement is true, give a proof. If it is false then write its negation and prove it.


Assume all sets are subsets of a universal set U.





For all sets A, B,and C, A-(B-C) = (A-B)-CDetermine if the statement is true or false and prove it. For all sets A, B,and C, A-(B-C) = (A-B)-C.?
Let A = {1,2,3}, B = {1,2} and C = {2,3}.





Then A - (B - C) = A - {1} = {2,3}, but (A - B) - C = {3} - {2,3} = 桅.





The statement is false, because the negation of a statement that starts with ';for all'; would be there exists at least one instance where it doesn't work. That is all you need to show, that there exist sets A, B and C such that A-(B-C) = (A-B)-C is not true. I gave you one such example, but there are many, many you could come up with.Determine if the statement is true or false and prove it. For all sets A, B,and C, A-(B-C) = (A-B)-C.?
false ; counterexample is A = reals , B = C = rationals....A -(B-C) = reals 鈺?(A-B) - C = irrationals....for discrete let A = integers in [1,50] and B = C = odds...A-(B-C) = all integers in [1,50] 鈺?(A-B) - C = evens in [1,50]

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