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De Morgan's Laws
Continuing with the relationship between ∧ and ∨, we can also use De Morgan's Law to rearrange sentences involving negation in conjunction with these connectives. Actually, there are 2 equivalences which taken as a pair are called De Morgan's Law:
¬(P ∧Q) ≡ ¬P ∨¬Q
¬ (P ∨ Q) ≡ ¬P ∧ ¬Q
These are essential rules and it is good spending some time thinking regarding why they are true.
Contraposition
The contraposition equivalence is following:
P -> Q ≡ ¬Q -> ¬P
At first, this can seem a little strange because it seem that we have said nothing in the first sentence regarding ¬Q, soin the second sentence how can we infer anything from it? However, imagine we know that P implies Q, and we saying that Q was false. In this case, if we were to imply that P was true because we know that P implies Q, we also know that Q is true. But Q was false .So we cannot possibly denote that P is true, which means that we ought to imply that P is false (because we are in propositional logic, so P might be either true or false). This argument shows that we may replace the first sentence by the second one, and it is left as aworkout to construct a similar argument for the vice-versa part of this equivalence.
Which techniques are utilized to gain on the number pairs and also explain how it helps in connecting number of subscribers. In rural areas, subscribers are usually dispersed.
Unification: As just above this we have said that the rules of inference for propositional logic detailed in the last lecture can also be required in first-order logic. Moreov
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