Propositional Logic Worksheet Page 15
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21Rearrangements of an Implication
Definition:
For conditional statement P → Q, the converse
statement is Q → P , the contrapositive statement is ¬Q → ¬P ,
and the inverse statement is ¬P → ¬Q.
Note: As we saw in a previous example, we can use a truth table to
determine if two compound propositions are logically equivalent,
ie if they always have the same truth values. If two propositions R
and S are logically equivalent, we write R ≡ S.
Example: Use a truth table to determine whether or not the con-
verse, contrapositive and inverse statements are logically equivalent
to P → Q.
Definition: If a compound proposition is always true, it is a tau-
tology. Note that if R ↔ S is a tautology, then R ≡ S.
Note:
≡ is not a logical connective and R ≡ S is not a com-
pound proposition. R ≡ S just means that R → S is a tautology.
Alternate notation: R ⇔ S.
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