Question

If A, B are nonempty sets, and A ⊂ B, prove that A
'
⊂ B'

Answer 1

Your mean is A dont have any thing and B too ?

Answer 2

If it was your mean so A'=M
And B'=M
too :)
Got it ?:)

Answer 3

What is mean?

Answer 4

do you know M ?

Answer 5

no we didn't study it yet

Answer 6

OK !
The M have all !
OK ?:)
M means mother and have all :)
Got it ?:)

Answer 7

ok

Answer 8

btw A' is the set that contains all limit points of A

Answer 9

Exacly !
Because \[A=\phi\]

Answer 10

It was =

Answer 11

And if we have B such as A so can say A=B
OK ?:)

Answer 12

@user917:Got it ?:)

Answer 13

But why A=ϕ ?

Answer 14

Because u say that in problem :)

Answer 15

That wasnt your mean ?????????

Answer 16

I said A, B are NONEMPTY set

Answer 17

OK !
Are they =M ??or just none empty ?

Answer 18

But dont need to know that :)
Wait ...

Answer 19

Look A'= the things are not in A , A' have then :
AUA'=M
OK ?:)
GOT it :)?

Answer 20

@user917:huh ????

Answer 21

and then?

Answer 22

Got that ?:)

Answer 23

wait a minute.. if A= { 2,85, 100} what is A' in this case?

Answer 24

A' have all the things M has except 2,85,100
oK ?

Answer 25

ok in this case if A is a bigger set than B that mean B' is a bigger set than A'

Answer 26

what ???

Answer 27

I think you're confusing between A' notation and A bar notation

Answer 28

A' is the set that contain all the LIMIT points of A

Answer 29

limit ???

Answer 30

Yes, a point p is called a limit point of a set E if every deleted
nbhd of p intersects E.

Answer 31

LOOK !:
If we have :
M:{1,2,3,4,5,6}
then
A:{1,2}
A':{3,4,5,6}
OK ??...

Answer 32

Are you sure?

Answer 33

I m sure :)
Just remember this :)

Answer 34

ok continue please :)

Answer 35

OK !
Now if A ⊂ B so B'⊂ A'
Because :
If we have :
M:{1,2,3,4,5,6,7,8,9}
B;{1,2,3,4,5,6}
A:{1,2,3}
A ⊂ B
So
A':{4,5,6,7,8,9}
B':{7,8,9}
So
B'⊂ A'
OK ?

Answer 36

@user917:Got that ?:)

Answer 37

Yes I got it

Answer 38

but the question was prove that A' ⊂ B' and not B' ⊂ A'

Answer 39

Sorry but I think you miss understand the question

Answer 40

A' is not A bar

Answer 41

OK !
I think the proof say :
The A' ⊂ B' is not right :)

Answer 42

Remember always M have both of A&A' and AUA'=M

Answer 43

M have both A & A bar

Answer 44

A&A'