Proving or Disproving (A-B)'=B'-A' in (a-b) Homework | Steps & Examples

[kathrynag]

Homework Statement

Prove or disprove:

(A-B)'=B'-A'

Homework Equations

The Attempt at a Solution

Let x$$\in$$(A-B)'
Then x$$\notin$$(A-B)
I'm not sure where to go from here...

 

[Mark44]

What's the context here? What are A and B? What does (A - B)' mean?

 

[VeeEight]

A-B is the set of elements in A that are not in B
So x is not in A-B means that x is in A but is not in B

You may want to try to think of some counterexamples before trying to show inclusion both ways.

 

[kathrynag]

A-B is the set of elements in A that are not in B
So x is not in A-B means that x is in A but is not in B

You may want to try to think of some counterexamples before trying to show inclusion both ways.

Ok so:
x$$\in$$A and x$$\notin$$B

Ok, so suppose A={1,2,3,4,5} B={3,4,6}
Then A-B={1,2,5}
So, (A-B)'={3,4,6}
so, (A-B)'=B

 

[VeeEight]

If you are working in R, then the complement of the set A-B would be R - {1, 2, 5}
You might want to try some simpler examples like A= (0,1) or {1, 2, 3} and B = [0,1] or {3, 4}

 

[kathrynag]

If you are working in R, then the complement of the set A-B would be R - {1, 2, 5}
You might want to try some simpler examples like A= (0,1) or {1, 2, 3} and B = [0,1] or {3, 4}

A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}

 

[VeeEight]

Okay.

 

[kathrynag]

A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}

Okay.

So, if x is not an element of A-B, then x is not an element of {1,2}

 

[kathrynag]

Homework Statement

Prove or disprove:

(A-B)'=B'-A'

Homework Equations

The Attempt at a Solution

Let x$$\in$$(A-B)'
Then x$$\notin$$(A-B)
I'm not sure where to go from here...

Ok, so

A={1,2,3}
B={3,4}
universe ={1,2,3,4,5,6,7}
A-B={1,2}
(A-B)'={3,4,5,6,7}

So, if x is not an element of A-B, then x is not an element of {1,2}

x$$\in$${3,4,5,6,7}
So x$$\notin$$A and x$$\in$$B

 

[pizzasky]

A = {1,2,3} , B = {3,4} , universe = {1,2,3,4,5,6,7}

A-B = {1,2}
(A-B)' = {3,4,5,6,7}

Keep going! What are A' , B' and B'-A' ?

 

[kathrynag]

a={1,2,3}
b={3,4}
universe ={1,2,3,4,5,6,7}
a-b={1,2}
(a-b)'={3,4,5,6,7}

keep going! What are a' , b' and b'-a' ?

a'={4,5,6,7}
b'={1,2,5,6,7}
b'-a'={1,2}

 

[kathrynag]

Still not quite sure
Let x$$\in$$(A-B)'
x$$\notin$$(A-B).
Can I say now x$$\in$$B? this is the part that confuses me...