De Morgan s Law

De Morgan's laws are two rules in Boolean algebra that relate to the logical operators "AND" and "OR". The laws are as follows:

1. The complement of the conjunction of two statements is equivalent to the disjunction of their complements. In other words, ~(A ∧ B) ≡ ~A ∨ ~B.

2. The complement of the disjunction of two statements is equivalent to the conjunction of their complements. In other words, ~(A ∨ B) ≡ ~A ∧ ~B.

These laws can be used to simplify logical expressions and to convert between different forms of expressions. For example, if we have the expression ~(A ∧ B), we can use De Morgan's first law to rewrite it as ~A ∨ ~B. Similarly, if we have the expression ~(A ∨ B), we can use De Morgan's second law to rewrite it as ~A ∧ ~B.