Understanding the role of empty sets when calculating set difference

Hi guys,

Lets say I have two sets:

A = { 0, 1, 2 } (where 0 represents the empty set, I don't know how to include the appropriate symbol)

B = { 1, 4 }

I am asked for the set difference: A - B.

I understand what is asked, I must list which elements are elements of A but not elements of B.

What is throwing me a bit is the fact that they listed the empty set as an explicit member of A.

Would the correct answer be:

A - B = { 0, 2 }

or

A - B = { 2 }

I understand that the empty set is a proper subset of any set and that when you calculate the powerset you will always list the empty set as one of the elements, but why include the empty set in A like my lecturer did here?

Thank you in advance for any help with this.

Re: Understanding the role of empty sets when calculating set difference

Quote:

Originally Posted by

**armitage75** Hi guys,

Lets say I have two sets:

$\displaystyle A = \{ \emptyset, 1, 2 \}$ (where 0 represents the empty set, I don't know how to include the appropriate symbol)

$\displaystyle B = \{ 1, 4 \}$

I am asked for the set difference: A - B.

I understand what is asked, I must list which elements are elements of A but not elements of B.

What is throwing me a bit is the fact that they listed the empty set as an explicit member of A.

Would the correct answer be:

A - B = { 0, 2 }.

[TEX]\emptyset [/TEX] gives $\displaystyle \emptyset $

The correct answer is $\displaystyle A-B=\{\emptyset,2\}$. You see that set $\displaystyle A$ gas three elements.

Re: Understanding the role of empty sets when calculating set difference

Hi Plato,

Thank you very much for your answer.

This clears it up for me :)