Question:
The Boolean expression \(\overline{(A+B+C)}\) is equal to
The Boolean expression \(\overline{(A+B+C)}\) is equal to
Show Hint
De Morgan's laws:
\[
\boxed{
\overline{A+B}=\bar{A}\,\bar{B}
}
\]
\[
\boxed{
\overline{AB}=\bar{A}+\bar{B}
}
\]
Updated On: Jul 14, 2026
- \(\bar{A}+\bar{B}+\bar{C}\)
- \(A(B+C)\)
- \((A+B)C\)
- \(\bar{A}\,\bar{B}\,\bar{C}\)
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The Correct Option is D
Solution and Explanation
Step 1: Apply De Morgan's theorem.
According to De Morgan's law,
\[
\overline{X+Y+Z}
=
\bar{X}\,\bar{Y}\,\bar{Z}.
\]
Step 2: Substitute the variables. Therefore, \[ \overline{(A+B+C)} = \bar{A}\,\bar{B}\,\bar{C}. \] Hence, \[ \boxed{\bar{A}\,\bar{B}\,\bar{C}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
Step 2: Substitute the variables. Therefore, \[ \overline{(A+B+C)} = \bar{A}\,\bar{B}\,\bar{C}. \] Hence, \[ \boxed{\bar{A}\,\bar{B}\,\bar{C}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
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