What would be yielded after simplifying the following Boolean expression:

Y = \(\rm\overline{(A+\bar{B}+C)+(B+\bar{C})}\)

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MPPKVVCL Indore JE Electrical 21 August 2018 Official Paper
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  1. Y = (A̅BC̅) + (B̅C)
  2. Y = (A̅ + B + C̅) (B̅ + C)
  3. Y = 0
  4. Y = 1

Answer (Detailed Solution Below)

Option 3 : Y = 0
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Detailed Solution

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Concept

1.) De-morgan's law: \(\overline{A+B}=\overline{A}\space\overline{B}\)

2.) \(\overline{A}{A}=0\)

3.) \(\overline{A}+{A}=1\)

Explanation

\(Y=\rm\overline{(A+\bar{B}+C)+(B+\bar{C})}\)

Using De-morgan's Law:

\(Y=\overline{(A+\overline{B}+C)}\space \overline{(B+\overline{C})}\)

\(Y=(\overline{A}B\overline{C})\space (\overline{B}C)\)

\(Y=\overline{A}(B\overline {B})(C\overline {C})\)

Y = 0

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