Boolean logic deMorgans theorem

In summary, the conversation involves proving that two expressions, X = A(B+C) and X = A' + B'C', are inverses of each other using deMorgan's theorem. The person asking for help is having trouble with this and is seeking assistance.
  • #1
fran1942
80
0
Hello, I am trying to prove that the following two expressions are the inverse of each other by using deMorgan's theorem.

i) X = A(B+C)
ii) X = A' + B'C'

I am having trouble doing this. Can this actually be achieved with these two expressions ?

Thank you for any help.
 
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  • #2
fran1942 said:
Hello, I am trying to prove that the following two expressions are the inverse of each other by using deMorgan's theorem.

i) X = A(B+C)
ii) X = A' + B'C'

I am having trouble doing this.
It is confusing the way you have written this, fran1942.

I think you'll find the question should be something like:

If X = A(B+C), apply de Morgans's theorem to show that X' = A' + B'C'
 

What is Boolean logic deMorgan's theorem?

Boolean logic deMorgan's theorem is a fundamental rule in Boolean algebra that states that the negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations of the individual terms.

Why is Boolean logic deMorgan's theorem important?

Boolean logic deMorgan's theorem is important because it allows for the simplification of complex logical expressions. It also helps in converting between different logical operators.

How is Boolean logic deMorgan's theorem applied?

Boolean logic deMorgan's theorem is applied by replacing the negation of a conjunction with the disjunction of the negations of individual terms, and vice versa. This allows for simplification of logical expressions and can also help in determining the equivalence of two logical statements.

Can Boolean logic deMorgan's theorem be used with more than two terms?

Yes, Boolean logic deMorgan's theorem can be used with any number of terms. The theorem states that the negation of a conjunction is equivalent to the disjunction of the negations of individual terms, regardless of the number of terms involved.

What is an example of using Boolean logic deMorgan's theorem?

An example of using Boolean logic deMorgan's theorem is simplifying the expression ¬(A ∧ B) to ¬A ∨ ¬B. This allows for easier evaluation and manipulation of logical statements.

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