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/sci/ - Science & Math

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5983679 No.5983679 [Reply] [Original]

I hate to do this but I'm really struggling, /sci/.

How do I prove Au(A'uB) = AuB

I'm sure this is pretty embarrassingly easy but I just signed up for Abstract Algebra and just don't know what to do.

>> No.5983681

Drawing a Venn diagram is by far the easiest way.

Otherwise, just assume something is an element in the first set, then show it must belong to the second. Then repeat the other way around.

>> No.5983730

Au(A'uB) = U

>> No.5983775

>>5983679

Hello!

As another poster pointed out, the union you have written is the full ambient set (universe). If you change your union into logical statements, say A is "statement A" and B is "statement B" then you are asking what is the set of things for which

statement A is true OR statement A is not true OR statement B is true


Evidently everything satisfies the first two conditions, and so you get everything--regardless of what B is.

I hope that helps!