बूलियन के नियम से सिद्ध कीजिए (A+B)(A+C) (B+C)=(A+B)(A+C)
Answers
Annulment Law – A term AND´ed with a “0” equals 0 or OR´ed with a “1” will equal 1
A . 0 = 0 A variable AND’ed with 0 is always equal to 0
A + 1 = 1 A variable OR’ed with 1 is always equal to 1
Identity Law – A term OR´ed with a “0” or AND´ed with a “1” will always equal that term
A + 0 = A A variable OR’ed with 0 is always equal to the variable
A . 1 = A A variable AND’ed with 1 is always equal to the variable
Idempotent Law – An input that is AND´ed or OR´ed with itself is equal to that input
A + A = A A variable OR’ed with itself is always equal to the variable
A . A = A A variable AND’ed with itself is always equal to the variable
Complement Law – A term AND´ed with its complement equals “0” and a term OR´ed with its complement equals “1”
A . A = 0 A variable AND’ed with its complement is always equal to 0
A + A = 1 A variable OR’ed with its complement is always equal to 1
Commutative Law – The order of application of two separate terms is not important
A . B = B . A The order in which two variables are AND’ed makes no difference
A + B = B + A The order in which two variables are OR’ed makes no difference
Double Negation Law – A term that is inverted twice is equal to the original term
A = A A double complement of a variable is always equal to the variable
de Morgan´s Theorem – There are two “de Morgan´s” rules or theorems,
(1) Two separate terms NOR´ed together is the same as the two terms inverted (Complement) and AND´ed for example: A+B = A . B
(2) Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and OR´ed for example: A.B = A + B