Question on Laws of sets (not sure which forum to post in)

[bushra1175]

I was looking at this example in the textbook and I don't understand how the expression changed from the second-last to the last line using the laws of sets (please see the purple arrow). I have included the laws of sets in the textbook for reference. I understand all the laws used up until that point.







I'm struggling to identify which law was applied as the results don't match any. All help will be greatly appreciated.

 

[linux-man]

Last step is using law 4. In this case, A is (A' ∪ B').

 

[Dr.Peterson]

I was looking at this example in the textbook and I don't understand how the expression changed from the second-last to the last line using the laws of sets (please see the purple arrow). I have included the laws of sets in the textbook for reference. I understand all the laws used up until that point.

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I'm struggling to identify which law was applied as the results don't match any. All help will be greatly appreciated.

Thanks for including all necessary information!

It's your law 4, \(A\cap U=A\). (Together with the commutative law, implicitly.) This is really a special case of 20.

 

[bushra1175]

Thanks for including all necessary information!

It's your law 4, \(A\cap U=A\). (Together with the commutative law, implicitly.) This is really a special case of 20.

That is so obvious its embarassing. Thank you!

 

[Steven G]

(A' ∪ B') is some set. The universal set U has all the elements for this problem. Now which elements are in both (A' ∪ B') and U. Surely the answer is (A' ∪ B') because every element in (A' ∪ B') is in U