Question

Can somebody help me on a set theory question, it has me lost.

Answer 1

Attached file is the question

Answer 2

@mathmale

Answer 3

My Set theory isn't too strong. But I believe C n A means the set that is an intersection, that is both in A and C. Same with B. However you can have A = / = B, because they only need to contain identical elements, but can contain more than just those needed.

Answer 4

What is A = / = B supposed to mean?

Answer 5

A does not equal B.

Answer 6

oh okay

Answer 7

so what would the counter example be?

Answer 8

A counter example can be as follows: C = {1,2,3,4,5}, A = {4,3,7,8}, B = {9, 6, 3, 4, 7}

Then C n A = {3, 4} = C n B, but we can see A =/= B

Answer 9

Oh, I guess that makes sense

Answer 10

So how can we make A = B with an extra condition?

Answer 11

@Angelina_Vella Gimme a min or two.

Answer 12

Okie, take your time, i'll see if I can figure anything out

Answer 13

I don't see anything really

Answer 14

@Angelina_Vella Me neither. :C

Answer 15

any ideas @zepdrix ?

Answer 16

I see that there's a possible counter example but i'm not sure how come up with another condition.

Answer 17

No ideas :/

Answer 18

?

Answer 19

@ganeshie8

Answer 20

Nevermind.

Answer 21

:(

Answer 22

We can try a different question if this one is too difficult?

Answer 23

For part a, you may try this :

\(C\cap A = C\cap B\) does not imply \(A = B\).
(You can cookyp a counterexample easily)

The extracondition that is required here is \(C\cup A = C\cup B\)

Answer 24

why C ∪ A = C ∪ B?

Answer 25

You tell me. Try describing or proving below statement if possible :
\( (C\cap A = C\cap B ) \land (C\cup A = C\cup B) \implies A = B\)

Answer 26

okay I can really just understand it in venn diagrams

Answer 27

Would you agree that \[\begin{align}
A &= A\cup (C \cap A) \\~\\
\end{align}\]

?

Draw a venn diagram if you want..

Answer 28

kinda hard to draw in parts

Answer 29

Check this
http://math.stackexchange.com/questions/1468080/unions-and-intersections-a-cup-b-a-%E2%88%AA-c-land-a-cap-b-a-%E2%88%A9-c-implies

Answer 30

ill try drawing out the one you said

Answer 31

There are plenty proofs in that link. Pick the one that you like and we may discuss if you have further questions...