Darren T.

asked • 06/26/17

For Set Functions how do I prove (A' U B') n B is = B - A

Question on the topic of Sets in Calculus where (A' U B') n B = B-A has to be proven true using formal mathematic logic

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Tom K. answered • 06/26/17

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B - A = BA'
 
(A' U B') n B = A'B U B'B = A'B = BA'
 
Thus, LHS = RHS
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Darren T.

How do I prove B - A = BnA'
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06/26/17

Philip P.

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You can also try using a truth table, noting that B - A = B∩A'.  If the truth values are identical, then they are equal.
 
A    B    A'    B'    (A'UB')  (A'UB')∩B  =  B∩A'
----------------------------------------------------
0    0     1     1        1           0       =        0
1    0     0     1        1           0       =        0
0    1     1     0        1           1       =        1
1    1     0     0        0           0       =        0
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06/26/17

Darren T.

Ok thank you very much!
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06/26/17

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