Are Disjoint Set Assertions Commutative?

Question

If I were to say that A intersect B was the empty set, does that imply that B intersect A is also the empty set?

Answer 1

Yes.

Because $A \cap B = \{ x | x \in A \text{ and } x \in B \}$ and surely "and" is commutative.

Answer 2

A ∩ B := {(x ∊ U)|(x ∊ A) ⋀ (x ∊ B)} You can see that this is a logical statement of the form P ⋀ Q and any logic textbook will tell you that P ⋀ Q = Q ⋀ P, i.e. that ⋀ is commutative, that seems to me to be the justification.