# Set theory problem

1. Sep 5, 2007

### neelakash

1. The problem statement, all variables and given/known data

I have to prove that if A blis a subset of B then B' is a subset of A'.

2. Relevant equations

3. The attempt at a solution

I did:
Let x belongs to B but x does not belong to A
=>x does not belong to B' but x belongs to A'
Hence proved.

please tell me if I am correct.

2. Sep 5, 2007

### bomba923

Consider the contrapositive:
$$A \subseteq B \to \left( {x \in A \to x \in B} \right) \to \left( {x \notin B \to x \notin A} \right) \to B' \subseteq A'$$

Last edited: Sep 5, 2007
3. Sep 5, 2007

### HallsofIvy

Staff Emeritus
How does "x does not belong to B' but does belong to A' " prove B' is a subset of A'?
For example, if B' were {1, 2, 3, 4, 5} and A' were {5, 6, 7} then x= 6 is not in B' but is in A'. It is certainly not the case that "B' is a subset of A'"!

To prove "B' is a subset of A'", you must, using the definition, prove "If x is in B' then it is in A'.

If x is in B', then what can you say about x?

4. Sep 5, 2007

### neelakash

You are correct.I was wrong in that arguement.

Thanks to both of you.