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Which of the following is a Simplification law?
- a)M.(~M+N) = M.N
- b)M+(N.O) = (M+N)(M+O)
- c)~(M+N) = ~M.~N
- d)M.(N.O) = (M.N).O
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which of the following is a Simplification law?a)M.(~M+N) = M.Nb)M+(N....
Explanation:
The given options are different laws or rules of simplification in Boolean algebra. Boolean algebra is a mathematical structure that deals with binary variables and logical operations. It helps simplify logical expressions and circuits.
The correct option is 'A', which represents the law of absorption. This law states that if we have a logical expression of the form M.(~M N), then it can be simplified to just M.N.
Law of Absorption:
- M.(~M N) = M.N
This law is based on the concept of absorption, where the presence of one variable absorbs or nullifies the effect of the other variable.
Other Options:
Let's briefly explain the other options mentioned:
Option B:
- M (N.O) = (M N)(M O)
This option represents the law of distribution. It states that if we have a logical expression of the form M (N.O), then it can be simplified to (M N)(M O). This law is based on the distributive property.
Option C:
- ~(M N) = ~M.~N
This option represents the law of De Morgan's theorem. It states that the negation of a logical expression can be achieved by negating each individual variable and changing the logical operator. In this case, ~(M N) is equivalent to ~M.~N.
Option D:
- M.(N.O) = (M.N).O
This option represents the law of associativity. It states that the order of operations in a logical expression does not matter. In this case, M.(N.O) is equivalent to (M.N).O.
Conclusion:
Among the given options, option 'A' represents the law of absorption, which simplifies a logical expression by nullifying the effect of one variable. Hence, option 'A' is the correct answer.
The given options are different laws or rules of simplification in Boolean algebra. Boolean algebra is a mathematical structure that deals with binary variables and logical operations. It helps simplify logical expressions and circuits.
The correct option is 'A', which represents the law of absorption. This law states that if we have a logical expression of the form M.(~M N), then it can be simplified to just M.N.
Law of Absorption:
- M.(~M N) = M.N
This law is based on the concept of absorption, where the presence of one variable absorbs or nullifies the effect of the other variable.
Other Options:
Let's briefly explain the other options mentioned:
Option B:
- M (N.O) = (M N)(M O)
This option represents the law of distribution. It states that if we have a logical expression of the form M (N.O), then it can be simplified to (M N)(M O). This law is based on the distributive property.
Option C:
- ~(M N) = ~M.~N
This option represents the law of De Morgan's theorem. It states that the negation of a logical expression can be achieved by negating each individual variable and changing the logical operator. In this case, ~(M N) is equivalent to ~M.~N.
Option D:
- M.(N.O) = (M.N).O
This option represents the law of associativity. It states that the order of operations in a logical expression does not matter. In this case, M.(N.O) is equivalent to (M.N).O.
Conclusion:
Among the given options, option 'A' represents the law of absorption, which simplifies a logical expression by nullifying the effect of one variable. Hence, option 'A' is the correct answer.
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Community Answer
Which of the following is a Simplification law?a)M.(~M+N) = M.Nb)M+(N....
By Simplification Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y. By, De’ Morgan’s law ~(X+Y) = ~X.~Y. By commutative law we can say that A.(B.C) = (A.B).C.
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