Question

Hey guys i am working on subset theory and stuff like that. I need some help on this one. If A={1,2,34,...} and B={2,4,6,8,...}, then What does A-B equal

Answer 1

I assume you mean A = {1, 2, 3, 4, ... }, yes?

In any case, A - B means the set of the elements of A which are not elements of B.

So what are the numbers or elements in A that are not elements of B?

Answer 2

yes i mean that, so the answer would be 1 and 3 right?

Answer 3

{1, 3, 5, 7, 9, ....} , yes

Answer 4

so odd numbers

Answer 5

Right

Answer 6

Why the hell doesn't my teacher teach me it like this lol they try to make it sooo confusing. lol

Answer 7

Probably because I am a mathematician and your teacher most probably is not. :-)

Answer 8

Ok here is another one from my hw. What is n(A) for the set A={0,{1,2},4}.

Answer 9

What's the definition of n(A), the number of elements of the set A?

Answer 10

yes

Answer 11

So write down for me, one element per line, the members of the set A

Answer 12

0
...

Answer 13

well i don't understand why 1,2 have like their own parethisis

Answer 14

because it's a set

The members of the set are
0
{1, 2}
4

So the members are a mix of numbers -- 0 and 4 -- and of a set -- { 1, 2}

Answer 15

because a set need not have the same sort of thing in it always as members.

Answer 16

in any case, what then is n(A) for this A = {0, {1, 2}, 4}

Answer 17

ooooo ok ok

Answer 18

sooo the answer is 3

Answer 19

wow i definently tried to make that too hard

Answer 20

correct, 3.

Answer 21

damn man u a good mathmatician lol like you teach it in a way i understand

Answer 22

thanks iight the next one i have to like draw a venn diagram for you. Using set theory notation describe the shaded region provided in the Venn Diagram...

Answer 23

Meh ... that's harder to see. You might have to figure that one out by yourself.

Answer 24

yeah your right
its too hard to draw

Answer 25

ok this one is there like short cut to figure out how many proper subsets does the set F={0,1,2,3....,10} have?

Answer 26

Yes. Each element is either in the subset or it is not in the subset.

Consider the set G = {a, b}

Then the subsets are
- the empty set (neither a or be in the subset)
- {a} (a in, b out)
- {a, b} (a in, b in)
- {b} (a out, b in)

So for each element there are two possibilities.

Hence for G there were 2 x 2 = 2^2 possibilities; i.e., 4 subsets.

Now for your set there are 11 members, so there are 2 x 2 x .... subsets. What is this exactly?

Answer 27

2,048

Answer 28

if i just keep multiplying

Answer 29

That was 2^11 and you're exactly right, 2^11 = 2,048

So there's a general rule here. Suppose A is a set with n(A) members, a finite number.

Then the number of subsets of A is
\[2^{n(A)}\]

Answer 30

ooooo ok ok gotcha thanks man i really appreciate it

Answer 31

sure. 'good answer' appreciated.

Answer 32

i should of clicked that like 10000 times lol

Answer 33

Ok what about, For any set A, A ∪ ∅=______ and A ∩ ∅=______

Answer 34

the _______ is the line where the answer is supposed to gothats how it looks in my book

Answer 35

Well, what's the definition of those things and what do you think the answers are?

Answer 36

For any set A, A Union a empty set = i don't know, lol i mean i dono if i am looking for a number or letter or what

Answer 37

What does A union B mean?

Answer 38

elemnts are either in A or B or in both

Answer 39

Yes, so A union empty set is

Answer 40

oelements are either A or an empty set or both

Answer 41

...which is what? What elements are in the empty set?

Answer 42

the ones not in A lol i dono

Answer 43

If you're stuck with this sort of thing, take a concrete example to help you figure it out.

So let's take B = {1,2,3,4,5}

What is the union of B with the empty set?

Answer 44

By the way, the elements of the empty set are .... nothing, because it's the empty set, it has no elements.

Answer 45

well a empty set wouldn't be 1,2,3,4,5

Answer 46

No so for this particular set B\[B \cup \emptyset = ??\]

Answer 47

x:x is not 1,2,3,4,5

Answer 48

No. Back to defintions

Answer 49

Let X = {1, 2, 3} and Y = {3, 4, 5}. What is
\[X \cup Y\]?

Answer 50

so x u y is 1 and 3

Answer 51

numbers that are in either x y or both

Answer 52

No X union Y is the set whose members are in X or Y. So
\[X \cup Y = \{ 1, 2, 3, 4, 5 \}\]

Answer 53

oooo ok

Answer 54

So now suppose Y = empty set = {}. What is
\[X \cup Y = X \cup \emptyset = ???\]

Answer 55

Remember X = {1, 2, ,3}

Answer 56

Are you stuck?

Answer 57

I'm going to assume you are. So let me ask you this.
If X = {1,2,3} and Y = {4}
what is the union of X and Y?

Answer 58

Ok ... bye.

Answer 59

my bad man cpu died and i couldn't find the charger

Answer 60

so the union of x and y is 1,2,3,4 correct?