Question

Given A = {1, 2, 3, 4}, B = {4, 5, 6,}, and C = {2, 6, 7}. Evaluate each set
a) A ∩ B
b) A U C
c) B U C
d) (A U B) ∩ C
e) A U (B U C)
f) (A ∩ B) ∩ C
g) (A ∩ B) U C

Answer 1

So starting at the top:
A intersect B is everything in both A and B.

Answer 2

so it would be 4 thats in both

Answer 3

Correct, {4} is the answer to question a)

Answer 4

ok
now the U i am a little confused on that one.

Answer 5

is that everything that NOT in A and C?

Answer 6

A union B is all the items that are in A or in B (or both)

Answer 7

ok.. that makes sense..

Answer 8

Oh, sorry the question is A union C

Answer 9

So all the items in A, or C, or both.

Answer 10

so the answer would be 4 cuz they both have it

Answer 11

No. \(A\cup C\) = {1,2,3,4,6,7}

Answer 12

so Union means ever element in both ones

Answer 13

Because 1 is in A, 2 is in both, 3 is in A, 4 is in A, 6 is in C, 7 is in C.

Answer 14

No. Union means all the elements in EITHER.
Intersection means all the elements in BOTH.

Answer 15

the upside down U is intersection and the U is union right?

Answer 16

Right

Answer 17

ok

Answer 18

Try c)

Answer 19

that would be {6} cuz they B and C have it only same

Answer 20

B union C

Answer 21

Not the ones in both, the ones in either

Answer 22

wait
B U C={2,4,5,6,7}

Answer 23

Right

Answer 24

Next one.

Answer 25

First do A union B then take the intersection of that and C.

Answer 26

A={1,2,3,4}
B={4,5,6}
(A U B={1,2,3,4,5,6}
C={2,6,7}
(A U B) ∩ C={2,6}

Answer 27

right?

Answer 28

Right!

Answer 29

YES!!!!!! :) :) :) i think im finally getting this .. woo hooo.. lol

Answer 30

I think you are also. Go for the next one.

Answer 31

so heres a question. do ( ) first right? then do the rest of problem?

Answer 32

Yep stuff in parens is evaluated first.

Answer 33

ok
working on problem.. give me minute

Answer 34

) A U (B U C)
B={4,5,6}
C={2,6,7}
(B U C)={2,4,5,6,7}
A={1,2,3,4}
answer A U (B U C)= {1,2,3,4,5,6,7}

Answer 35

right? :)

Answer 36

polpak?

Answer 37

Sorry, one sec

Answer 38

np

Answer 39

Yes, that is right

Answer 40

YES!~ i think im finally getting this.. about damn time.. lol only taking college math for the 2nd time lol

Answer 41

I've been there ;)

Answer 42

it sucks.. and its a required class.. :(

Answer 43

Oh, no. Math is great. Just keep at it. You're doing well

Answer 44

e) A U (B U C)
B={4,5,6}
C={2,6,7}
(B U C)={2,4,5,6,7}
A={1,2,3,4}
answer A U (B U C)={1,2,3,4,5,6,7}

Answer 45

Isn't that the one you already did?

Answer 46

no this is a different one.. lol

Answer 47

lol yea it was the same.. my bad.. lol

Answer 48

but good job doing it right twice in a row. means you definitely get it ;)

Answer 49

lol
ok so the upside down means everything that is the same right? just wanted to make sure i got this correct .. :)

Answer 50

the intersection operator \(\cap\) means everything that is in BOTH. If it is just in one, or the other it doesn't count. It has to be in both.

Answer 51

f) (A ∩ B) ∩ C
A={1,2,3,4}
B={4,5,6}
(A ∩ B)={4}
C={2,6,7}
answer (A ∩ B) ∩ C={4}

Answer 52

wait this is a trick one.. cuz there is nothing that is in both

Answer 53

There is nothing that is common to A, B and C. So the intersection will be the empty set, {}

Answer 54

ok

Answer 55

Good catch

Answer 56

g) (A ∩ B) U C
A={1,2,3,4}
B={4,5,6}
(A ∩ B)={4}
C={2,6,7}
answer (A ∩ B) U C={2,4,6,7}

Answer 57

Right

Answer 58

sweet! i finally got this type of problems down.. :) whoo hooo .. lmao Thank you for taking the time to teach me this stuff.. :)

Answer 59

Of course! Happy to help =)

Answer 60

Using correct mathematical notation and symbols, express the following in set-builder notation: Z = {8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}

Answer 61

im not sure how to do this ?

Answer 62

It's trying to get you to write it in a more compact way.

Answer 63

ok... i dont know how else to write it..lol

Answer 64

Ok, there isn't a general way to explain set builder so I'll just show you and explain how to do this one and you'll hopefully get the idea.

Z = \(\{ x | (x \in \mathbb{N} )\wedge (8 \le x \le 18)\} \)

Answer 65

Do you know all those symbols?

Answer 66

hmmmm no... :(

Answer 67

Ok I'll list them:

| means 'such that'
\(\in\) means 'is an element of'
\(\mathbb{N}\) is the set of natural numbers (1,2,3,4,... etc)
\(\wedge\) means 'and'
\(\le \) means 'less than or equal to'

Using that translation, convert what I wrote into an english sentence.

Z is the set of ...

Answer 68

Just throw something out and I'll correct as needed.

Answer 69

i am confused.. sorry

Answer 70

what is x again? u dont have it listed

Answer 71

x is just a variable called x

Answer 72

i am very confused sorry.. :( on the whole thing..

Answer 73

Ok I'll translate, you compare what I say to the symbol version as well as the original version and see if it makes sense:

Original:
Z = {8,9,10,11,12,13,14,15,16,17,18}

Set builder:
Z=\(\{ x | (x \in \mathbb{N} )\wedge (8 \le x \le 18)\}\)

English:
Z is the set of numbers x such that x is in the natural numbers and x is between 8 and 18 inclusive.

Answer 74

so x would be 8,9,10,11,12,... ect

Answer 75

such as the natural numbers

Answer 76

ok i am starting to kinda understand this.. "kinda" lol

Answer 77

Yes. It would have to be in order to match the original set.

Answer 78

ok...

Answer 79

But we don't want all the natural numbers because then we'd have 1, 2, and 3, along with 3076, etc.

Answer 80

so we say that x has to be in the natural numbers and has to be between 8 and 18.

Answer 81

oh ok...

Answer 82

But we have to say x is in the natural numbers. If we just said x was between 8 and 18 it would include numbers like 17.1254

Answer 83

or 9.15

Answer 84

we only want the 'whole' numbers

Answer 85

ok now i understand it

Answer 86

ty sweetie!

Answer 87

Certainly

Answer 88

:)