Using De Morgan’s law, what is the equivalent of the $\overline{( P . Q . R )}$??
$\overline{P} + \overline{Q} + \overline{R}$
To solve this problem, we need to understand and apply De Morgan's Laws, which are fundamental rules in Boolean algebra used for simplifying expressions.
De Morgan's Laws state the following:
- \overline{(A . B)} = \overline{A} + \overline{B}
- \overline{(A + B)} = \overline{A} . \overline{B}
Given the expression: \overline{( P . Q . R )}
We apply De Morgan's first law, which is a generalization for any number of variables:
\overline{( P . Q . R )} = \overline{P} + \overline{Q} + \overline{R}
Let's break this down step-by-step:
- According to De Morgan's Law, the negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations.
- Thus, for three variables combined using AND, like P . Q . R, the negated form is the OR of the individual negated variables.
- This simplification results in: \overline{P} + \overline{Q} + \overline{R}
Therefore, the equivalent expression for \overline{( P . Q . R )} using De Morgan’s law is \overline{P} + \overline{Q} + \overline{R}.
The correct answer is: \overline{P} + \overline{Q} + \overline{R}
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