Question

please help @Falco276 @jim_thompson5910 @dumbcow

Answer 1

this is the question please

Answer 2

You know what those operators \(\cup\) and \(\cap\) mean?

Answer 3

no

Answer 4

addition and multiplication??

Answer 5

They mean union and intersection, respectively.
Union is *similar* to addition
while
intersection means 'elements in common'

Answer 6

ok.so can you help me answer those questions

Answer 7

Here's an example...
X = {1,2,3,4,5,6,7}
Y = {2,4,6,8,10}

The union of X and Y would be all their elements, together...
\[X\cup Y = \left\{1,2,3,4,5,6,7,8,10\right\}\]
But their intersection would be only the elements that they share...
\[X \cap Y = \left\{2,4,6\right\}\]

Answer 8

yes i know that but i have a problem with the question i posted thats why i need help

Answer 9

Let's try the first one, \(A \cup B\)
So, what do A and B correspond to?

Answer 10

all the elements in A ND B

Answer 11

That's right.
And you know how many elements there are in A and in B...so what do you do to them to get the *union*?

Answer 12

WRITE THEM ALL OUT

Answer 13

No... you're not asked to write out the elements, you're just asked HOW MANY elements are in the union...

Answer 14

And easy on the caps lock, mate :)

Answer 15

lol

Answer 16

oh ok.so i write 4?

Answer 17

Why 4?

Answer 18

cos group A has 2 likewise B

Answer 19

OR NO I ADD THEM ALL UP

Answer 20

How do you figure that group A has 2?

Answer 21

i have changed my mind,i need to add the elements in A up and the same for B

Answer 22

And you get...?

Answer 23

138137

Answer 24

That's right :)

Answer 25

YAY..THEN TO B

Answer 26

Now the second one.... is trickier...
You have to do them one at a time...
So...
\[\Large E\cap (C\cup D)\]

Answer 27

So, this part\[\Large E\cap \color{blue}{(C\cup D)}\]means the elements in C or D, like in part (a).
However, this part here
\[\Large \color{red}{E\cap} (C\cup D)\]
Means you only take the elements in C or D *that are also in E*
Or in other words, only Marines and Navy-units that are ENLISTED. (no officers)

Answer 28

Ok so what is the answer.

Answer 29

You lost me there :P

Answer 30

LOL Just kidding. That red part there only means you add the parts that are in the (E) row
\[\Large \color{red}{E\cap} (C\cup D)\]

Answer 31

so u mean the answer is 52448

Answer 32

That is correct :P

Answer 33

den the next questiion

Answer 34

Now to (c)
I missed introducing that prime \(\prime\) operator. It simply means "not"
so
O' means "not in O"
and
B' means "not in B"

Answer 35

oh ok

Answer 36

therefore...lol

Answer 37

Well, what does it mean, to 'not be in O'

Answer 38

then in E

Answer 39

Correct.
So only count the ones in E.
Now, what does it mean to not be in B?

Answer 40

IN A C ND D

Answer 41

Good, so, now you take the intersection.
You want those in E, but also in either A, C, or D.

Add them up.

Answer 42

so with those in E i need not add B in it

Answer 43

Yup, that's another way to look at it :)

Answer 44

did u say i needed to find the intersection

Answer 45

Intersection, yes.
So that just means elements in E *and* in B' (which means not in B)

Answer 46

so i would have
O prime as 57825,42400.10049

Answer 47

Yup... that's actually already O' \(\cap\) B'

Answer 48

and B prime as ??

Answer 49

oh so that is the answer

Answer 50

No, O' is all of E. (B included)
But since you intersected it with B', then you have to take away the B.

Answer 51

so im right on that one?

Answer 52

Depends... what's your answer?

Answer 53

i need to add all of them up or

Answer 54

Yup.

Answer 55

110274

Answer 56

so with union and intersection i need to add up every time

Answer 57

Yes, with union, you simply add all the concerned, while with intersections, you need to do a little more thinking.

Mind you, this is a rather simple example, normally, taking unions/intersections isn't nearly as straightforward as this one...

Answer 58

oh ok.

Answer 59

i have another question

Answer 60

Yes?

Answer 61

let me tag you in it then