Set Theory Part 2

Set Theory Part 2

Multiple Select

Find the intersection:

{1,3,5,7,9} ∩ {2,4,6,8}.

• {1,2,3,4,5,6,7,8,9}

• {}

• ø

• {1,3,4,7,9}

Multiple Choice

Find the union:

{1,3,5,7,9} U ø

• {ø}

• {ø,1,3,5,7,9}

• This is not possible.

• {1,3,5,7,9}

​Random

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

​

​

​

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

Multiple Choice

Select which is A'.

Multiple Choice

Select which option is the same as this.

• (A U B)'

• (A' U B')

• (A U B')

• A U B'

• A' U B'

Multiple Choice

Select which is (A ∩ B)'.

Multiple Choice

Select which is A' ∩ B.

​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.

Multiple Choice

Select which is A U B'.

​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).

Multiple Choice

Select which is A' ∩ B'.

​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.

Multiple Choice

Select which option is the same as this.

• (A U B) U (A ∩ B)

• (A U B) U (A' ∩ B)

• (A U B) U (A' ∩ B')

• (A U B) U (A ∩ B')

Multiple Choice

Use words to describe:

1. S' ∩ T

• In T along with everything that's not in S.

• In all of T but not in S.

• In T but not in S.

• In T along with universal set.

Multiple Choice

Use words to describe:

2. S' U T'

• Everything except the intersection.

• Everything except the union.

• Everything

• Everything except the outside of the circles.

Multiple Choice

Use words to describe:

3. S' ∩ T'

• In S and in T.

• Not in S and not in T.

• Everything except the intersection.

• Only the intersection.

Multiple Choice

Use words to describe:

4. (S U T)'

• Everything except the intersection.

• Not in the intersection of S and T.

• Not in the union of S and T.

• Not in S but everything in T and U.

​Random

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

​

​

​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? 🙄

Multiple Select

U = {2, 4, 6, 8, 10}, P = {2,6,10}. Write:

1. Any set R with 3 elements such that P U R = {2,4,6,10}

• R = {4,6,10}

• R = {2,4,6}

• R = {4,8}

• R = {2,6,10}

• R = {2,4,10}

Multiple Choice

U = {2, 4, 6, 8, 10}, P = {2,6,10}. Write:

2. Any set T such that P U T' = {2,4,6,8,10}

• T = {2,6,10}

• T = {4,8}

• T = {2,4,6,8,10}

Multiple Choice

U = {2, 4, 6, 8, 10}, P = {2,6,10}. Write:

Any set L with 3 elements such that P' U L = Universal (U)

• L = {4,8]

• L = {2,4,6,8,10}

• L = ø

• L = {2,6,10}

Multiple Choice

Select which is A ∩ B ∩ C.

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

Multiple Choice

Select which is (A U B) ∩ (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}

​

​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.

Multiple Choice

Select which is A ∩ (B U C)

​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}

​

​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}