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Question

Using De Morgan’s law, what is the equivalent of the $\overline{( P . Q . R )}$??   

The correct answer is

$\overline{P} + \overline{Q} + \overline{R}$

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:

  1. According to De Morgan's Law, the negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations.
  2. Thus, for three variables combined using AND, like P . Q . R, the negated form is the OR of the individual negated variables.
  3. 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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Similar Questions

  1. In Boolean algebra, what is the value of C + C’?


Important Questions from Laws of Boolean Algebra

  1. Method of subtraction by an additive approach is known as ______ subtraction.

  2. Which type of Boolean algebra law do the following laws belong to?

    Law 1: A + A.B = A

    Law 2: A(A + B) = A

  3. The equality (A + B + C)I = AI.BI.CI is better known as _______

  4. What is the minimum number of NAND gates required to implement \( A +A\bar{B} + AB\bar{C}\)?

  5. Find out the equivalent of A + A' + B'.

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