Set Theory Part 2

• When performing set operations, always perform any operations inside the parentheses first!!!

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• ​"OR" refers to union, and "AND" refers to intersection.

​It's asking for everything that's not in A that intersects with B.

​The red colour represents everything that's not in A.

​The purple colour represents B. It asked for the intersection of both. Where purple and red intersect is the answer.

​This is asking for all of A along with everything that isn't in B.

​The purple represents all of A. The red represents everything that isn't in B. Because it said union and not intersection, we're gonna include (unite hehe) all the parts that are coloured. If it said intersection, we'd include A (only A).

​This is asking for everything that's not in A, everything that's not in B and where they intersect.

The colour blue represents everything that's not in A.​

​The green colour represents everything's not in B. Because it says intersection, we have to look at where the two colour intersect.

​What do you realize about S' ∩ T' and (S U T)'?

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​THEY ARE THE SAME.

​So basically what they did to S' ∩ T' was to say union instead and put the complement sign outside the brackets.

​***Pretend it's labelled S and T, okay? 🙄

​This is not the best explanation because it didn't say (A ∩ B) ∩ C. But, this was the only thing I can think of.

​For example:

A={1,2,3,4,5,6,7,8,9,10}, B={1,2,3,4,11,12,13}, C {1,2,5,6,11,12,15,16,17}

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​A U B = {1,2,3,4,5,6,7,8,9,10,11,12,13}

​B U C = {1,2,3,4,5,6,11,12,13,15,16,17}

​(A U B) ∩ (B U C) = {1,2,3,4,5,6,11,12,13} ALL OF B IS IN THIS

​The numbers 5 and 6 aren't it, but it's in A and C.

​ignore this if you dont get it.

​Purple represents B U C.

​The answer is wherever Orange intersects B U C.

​For example:

A={1,2,3,4,5,6,7,8,9,10}, B={1,2,3,4,11,12,13}, C={1,2,5,6,11,12,15,16,17}

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​B U C ={1,2,3,4,5,6,11,12,13,15,16,17}

​What elements do A and B U C share?

​A ∩ (B U C)={1,2,3,4,5,6}