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Commutatively of Connectives
You will be aware from the fact that some arithmetic operators have a property that it does not matter which way around you give the operator input. We call this property commutatively. For instance, when adding 2 numbers, it does not matter which one comes first, because a+b = b+a forall b and a. The similar is true for multiplication but not true for divisionand subtraction.
The ∧,∨ and <-> connectives (which operate on two sub sentences), also have the commutatively property. We can express this with 3 tautologies:
P ∧ Q ≡ Q∧ P
P ∨ Q ≡ Q ∨P
P <-> Q = Q <-> P
So, if it helps to do so, whenever we see P ∧ Q, we may rewrite it as Q ∧ P, and similarly for the other 2 commutative connectives.
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