Crosson said:Do you use xy to mean (x)(y) ?
If so you forgot to apply ((x)(y))' = x' + y'
If that doesn't make any sense it is because I made a bad guess at your notational conventions.
l46kok said:
So I thought how you do this is to invert the variables, and change the type of gate.
Therefore, I had
(xy)(xy)(yz')
But if I actually use real numbers to check.. this conversion is wrong.
Am I looking at the demorgan's theorem wrong? Please give me any suggestions
Demorgan's Theorem is a set of rules in Boolean algebra that describe how to simplify logical expressions. It states that the negation of a logical expression, when applied to each term, is equivalent to switching the logical operators and negating the entire expression.
Demorgan's Theorem is important because it allows us to simplify complex logical expressions into simpler ones. This makes it easier to analyze and evaluate logical statements, which is useful in fields such as computer science, mathematics, and engineering.
To apply Demorgan's Theorem, you first identify the logical operators (AND, OR, NOT) in the expression. Then, you switch the operators and negate each term. Finally, you simplify the expression by using basic algebraic rules.
One example of using Demorgan's Theorem is simplifying the expression ~(A ∨ B) to ~A ∧ ~B. Another example is simplifying the expression ~(A ∧ B) to ~A ∨ ~B. These examples show how the negation of a logical expression can be applied to each term and the operators switched.
Yes, Demorgan's Theorem can be applied to any logical expression that contains the logical operators AND, OR, and NOT. It is a universal rule in Boolean algebra and can be used to simplify any complex logical statement into a simpler form.