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Author: Admin | 2025-04-27
ADe Morgan’s Law(P + Q)’ = (P)’.(Q)’(P.Q)’ = (P)’ + (Q)’ Let’s learn about these laws in detail.Identity LawIn the Boolean Algebra, we have identity elements for both AND(.) and OR(+) operations. The identity law state that in boolean algebra we have such variables that on operating with AND and OR operation we get the same result, i.e.A + 0 = AA.1 = ACommutative LawBinary variables in Boolean Algebra follow the commutative law. This law states that operating boolean variables A and B is similar to operating boolean variables B and A. That is,A. B = B. AA + B = B + AAssociative LawAssociative law state that the order of performing Boolean operator is illogical as their result is always the same. This can be understood as,( A . B ) . C = A . ( B . C )( A + B ) + C = A + ( B + C)Distributive LawBoolean Variables also follow the distributive law and the expression for Distributive law is given as:A . ( B + C) = (A . B) + (A . C)Inversion LawInversion law is the unique law of Boolean algebra this law states that, the complement of the complement of any number is the number itself.(A’)’ = AApart from these other laws are mentioned below:AND LawAND law of the Boolean algebra uses AND operator and the AND law is,A . 0 = 0A . 1 = AA . A = AOR LawOR law of the Boolean algebra uses OR operator and the OR law is,A + 0 = AA + 1 = 1A + A = ADe Morgan’s Laws are also called De morgan’s Theorem. They are the most important laws in Boolean Algebra and these are added below under the heading Boolean Algebra TheoremBoolean Algebra TheoremsThere are two basic theorems of great importance in Boolean Algebra, which are De Morgan’s First Laws, and De Morgan’s Second Laws. These are also called De Morgan’s Theorems. Now let’s learn about both in detail.De Morgan’s First lawsDe Morgan’s Law states that the complement of the product (AND) of two Boolean variables (or expressions) is equal to the sum (OR) of the complement of each Boolean variable (or expression). (P.Q)’ = (P)’ + (Q)’The truth table for the same is given below:PQ (P)’ (Q)’(P.Q)’(P)’ + (Q)’ TTFFFFTFFTTTFTTFTTFFTTTTWe can clearly see that truth values for (P.Q)’ are equal to truth values for (P)’ + (Q)’, corresponding to the same input. Thus, De Morgan’s First Law is true.De Morgan’s Second lawsStatement: The Complement of the sum (OR) of two Boolean variables (or expressions) is equal to the product(AND) of the complement of each Boolean variable (or expression).(P + Q)’ = (P)’.(Q)’Proof:The truth
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