De Morgan’s Law
For statements p and q,⌐(p ᴧ q) ≡ ⌐p v ⌐q⌐(p v q) ≡ ⌐p ᴧ ⌐q
De Morgan’s law is a set of rules that shows how to form the negation of a logical condition that includes one or more simple conditions. Specifically, it deals with the negation of conjunctions and disjunctions and provides a way to rewrite them in a different form that may be easier to understand or work with.
There are two De Morgan’s laws:
1. The negation of a conjunction is a disjunction of negations:
– Example: ¬(A ∧ B) = ¬A ∨ ¬B
– This means that if we want to negate the statement A and B are both true, we can rephrase it as Either A is not true or B is not true.
2. The negation of a disjunction is a conjunction of negations:
– Example: ¬(A ∨ B) = ¬A ∧ ¬B
– This means that if we want to negate the statement Either A or B (or both) is true, we can rephrase it as Neither A is true nor B is true.
These laws can be useful in simplifying logical expressions, as they allow us to rewrite complex expressions in terms of simpler ones. Additionally, they can also be useful in proving mathematical theorems, particularly in areas such as set theory and boolean algebra.
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