# Thread:

1. ## Differences of sets

If the difference of sets A and B is the set containing elements that are in A but not in B and B is an all-inclusive set then is A-B={null set} or just A-B=null set?

I was thinking that it would be A-B={null set} since the definition of the difference of sets is that it is, "the set containing..."

Thanks!

2. Originally Posted by buddyp450
If the difference of sets A and B is the set containing elements that are in A but not in B and B is an all-inclusive set then is A-B={null set} or just A-B=null set?
I was thinking that it would be A-B={null set} since the definition of the difference of sets is that it is, "the set containing..."
I, for one, have no idea what you point is. What are you asking?
Here is a fact: $A \subseteq B\quad \Leftrightarrow \quad A\backslash B = \emptyset$.

3. I'm sorry, let me try to be more clear as I'm new to discrete mathematics.

A = {1, 2, 3, 4, 5}
B = {1, 2, 3, 4, 5}

so does

A-B = $\emptyset$

or

A-B = { $\emptyset$}

and could you please explain why?

4. ## Notation

Originally Posted by buddyp450
I'm sorry, let me try to be more clear as I'm new to discrete mathematics.

A = {1, 2, 3, 4, 5}
B = {1, 2, 3, 4, 5}

so does

A-B = $\emptyset$

or

A-B = { $\emptyset$}

and could you please explain why?
$\emptyset$ is equivalent to {}. This is standard notation. E.g., { $\emptyset$} is the set containing the empty set. So, A-B is $\emptyset$ or {}, not { $\emptyset$}.

5. Originally Posted by Plato
I, for one, have no idea what you point is. What are you asking?
Here is a fact: $A \subseteq B\quad \Leftrightarrow \quad B\backslash A = \emptyset$.
Is that a typo, or am I misunderstanding the notation? $\{1\}\subset\{1,2\}$ but $\{1,2\}-\{1\}=\{2\}$

6. I think that by "B is an all inclusive set" you mean that B is the universal set. In that case, everything is in B so "are in A but not in B" does not apply to anything since there is nothing that is "not in B". A- B is the empty set.
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