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Which of the following boolean algebra statements represent distributive law?
- a)(A + B) + C = A + ( B + C)
- b)A . (B + C) = (A . B) + (A . C)
- c)A . (B . C) = (A . B) . C
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Which of the following boolean algebra statements represent distributi...
Distributive Law in Boolean Algebra
Definition: Distributive law in boolean algebra is a rule that relates the three basic logical operations AND, OR, and NOT. It states that for any boolean expressions A, B, and C:
- A AND (B OR C) = (A AND B) OR (A AND C)
- A OR (B AND C) = (A OR B) AND (A OR C)
Explanation
The distributive law is an important concept in boolean algebra that is used to simplify boolean expressions. It allows us to distribute the AND and OR operations over each other, which can help in reducing the complexity of the expression. Let's take a look at the given options:
a) (A AND B) OR C = A OR (B OR C)
This is not an example of distributive law. It is actually an example of associative law, which states that the order of grouping of terms in an expression does not affect its value.
b) A AND (B OR C) = (A AND B) OR (A AND C)
This is an example of distributive law. It shows that we can distribute the AND operation over the OR operation.
c) A AND (B AND C) = (A AND B) AND C
This is an example of associative law, which states that the order of grouping of terms in an expression does not affect its value.
d) None of these
This is not a valid option as one of the given options is an example of distributive law.
Conclusion
In conclusion, option B is the correct answer as it represents the distributive law in boolean algebra. The distributive law is an important concept in boolean algebra that helps in simplifying boolean expressions.
Definition: Distributive law in boolean algebra is a rule that relates the three basic logical operations AND, OR, and NOT. It states that for any boolean expressions A, B, and C:
- A AND (B OR C) = (A AND B) OR (A AND C)
- A OR (B AND C) = (A OR B) AND (A OR C)
Explanation
The distributive law is an important concept in boolean algebra that is used to simplify boolean expressions. It allows us to distribute the AND and OR operations over each other, which can help in reducing the complexity of the expression. Let's take a look at the given options:
a) (A AND B) OR C = A OR (B OR C)
This is not an example of distributive law. It is actually an example of associative law, which states that the order of grouping of terms in an expression does not affect its value.
b) A AND (B OR C) = (A AND B) OR (A AND C)
This is an example of distributive law. It shows that we can distribute the AND operation over the OR operation.
c) A AND (B AND C) = (A AND B) AND C
This is an example of associative law, which states that the order of grouping of terms in an expression does not affect its value.
d) None of these
This is not a valid option as one of the given options is an example of distributive law.
Conclusion
In conclusion, option B is the correct answer as it represents the distributive law in boolean algebra. The distributive law is an important concept in boolean algebra that helps in simplifying boolean expressions.
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Community Answer
Which of the following boolean algebra statements represent distributi...
Distribution law:- A(B+C) = AB + AC (same as we use in basic maths)
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