1 Logical equivalence
तार्किक समकक्षता
When proving a proposition in mathematics it is often useful to look at a logical variation of the proposition in question that “means the same thing”. What does “meaning the same thing” mean? For our purposes, in keeping with our “meaning is truth, truth meaning” mantra, it will mean having the same truth-conditions. This is the notion of logical equivalence.
Definition 1.1. Two (possibly compound) logical propositions are logically equivalent if they have the same truth tables.
1.1 Contrapositive, converse and inverse
Definition 1.2. Given the implication P ⇒ Q, the implication (Not Q)⇒ (Not P) is called its contrapositive.
( Let’s show that the implication P ⇒ Q and its contrapositive ¬Q ⇒ ¬P are logically equivalent.)
तार्किक समकक्षता
When proving a proposition in mathematics it is often useful to look at a logical variation of the proposition in question that “means the same thing”. What does “meaning the same thing” mean? For our purposes, in keeping with our “meaning is truth, truth meaning” mantra, it will mean having the same truth-conditions. This is the notion of logical equivalence.
Definition 1.1. Two (possibly compound) logical propositions are logically equivalent if they have the same truth tables.
1.1 Contrapositive, converse and inverse
Definition 1.2. Given the implication P ⇒ Q, the implication (Not Q)⇒ (Not P) is called its contrapositive.
( Let’s show that the implication P ⇒ Q and its contrapositive ¬Q ⇒ ¬P are logically equivalent.)
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