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?
Are Disjoint Set Assertions Commutative?
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elementary-set-theory
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3How could this fail? (It is not a rhetorical question.) – 2011-01-19
2 Answers
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Yes.
Because $A \cap B = \{ x | x \in A \text{ and } x \in B \}$ and surely "and" is commutative.
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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.