DISCRETE: A-ø=? (A is defined)

[MelissaJL]

Homework Statement

Suppose A={ø,1,2,{1,2},{3}}. Determine if each statement is true or false. Give a brief justification for your answers.
(I finished the majority of them except for the last two)
g) A-ø=A
h) A-ø={1,2,{1,2},{3}}

Homework Equations

The definition of difference between two sets.
Let A and B both be sets. Then A-B={x: x\inA and x\notinB}

The Attempt at a Solution

So basically one of the questions is false and the other is true. Immediately I want to say (h) is true just because A has an empty set in it but after thinking about it I think (g) is true.
This is because we are trying compare what is in the empty set that A also contains... but the empty set has nothing in it so there is nothing to take from A. Therefore A-ø=A. Is this right? If it's not can someone explain to me why?
I'm getting quite conflicted as to which one I believe is true. Help understanding which is true would be greatly appreciated. :)

 

[Dick]

Homework Statement

Suppose A={ø,1,2,{1,2},{3}}. Determine if each statement is true or false. Give a brief justification for your answers.
(I finished the majority of them except for the last two)
g) A-ø=A
h) A-ø={1,2,{1,2},{3}}

Homework Equations

The definition of difference between two sets.
Let A and B both be sets. Then A-B={x: x\inA and x\notinB}

The Attempt at a Solution

So basically one of the questions is false and the other is true. Immediately I want to say (h) is true just because A has an empty set in it but after thinking about it I think (g) is true.
This is because we are trying compare what is in the empty set that A also contains... but the empty set has nothing in it so there is nothing to take from A. Therefore A-ø=A. Is this right? If it's not can someone explain to me why?
I'm getting quite conflicted as to which one I believe is true. Help understanding which is true would be greatly appreciated. :)

Think about the difference between A-ø and A-{ø}. ø (which has no elements) and {ø} (which has one element ø) are two different things. That might help.

 

[MelissaJL]

Thanks, so (g) is true and (h) is false. If (h) were to be true then it would be A-{emptyset}={1,2,{1,2},{3}}?

 

[Dick]

Thanks, so (g) is true and (h) is false. If (h) were to be true then it would be A-{emptyset}={1,2,{1,2},{3}}?

Yes, A-{ø}={1,2,{1,2},{3}}. A-ø=A. You were right.

 

[MelissaJL]

Thank you so much :)