# Math Help - Question about Sets and Logic

1. ## Question about Sets and Logic

List the elements of each set. Show all your work.
A = {1,2,5,6}
B = {2,5,7}
C= {1,3,5,7,9}
A ⊕ B and A ⊕ C
I am assuming the answer is {1,6,7} for A ⊕ B and {2,3,6,7,9} for A ⊕ C

Which includes everything that is not intersected.

Is this correct?

2. You are correct.

3. Is it ok to explain (A ⊕ B) as:

(A ⊕ B) = { x | x ∈ A ⊕ x ∈ B}

4. Originally Posted by robasc
Is it ok to explain (A ⊕ B) as:

(A ⊕ B) = { x | x ∈ A ⊕ x ∈ B}
No it is not.
$A \oplus B = \left( {A \cup B} \right)\backslash \left( {A \cap B} \right) = \left( {A\backslash B} \right) \cup \left( {B\backslash A} \right)$

That is called symmetric difference.

5. Is this the only one? Could I do this:

(A ∪ C) - B = {x | x ∈ (A ∪ C) or x ∉ B)

6. Originally Posted by robasc
Is this the only one? Could I do this:
(A ∪ C) - B = {x | x ∈ (A ∪ C) or x ∉ B)
I have no idea what in the world you are trying to do.
But it is (A ∪ C) - B = {x | x ∈ (A ∪ C) and x ∉ B)