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A programmable logic array (PLA) is shown in the figure.

GATE EC 2017 slot 2 part 2 D3

The Boolean function F implemented is

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GATE EC 2017 Official Paper: Shift 2
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  1. P¯Q¯R+P¯QR+PQ¯R¯
  2. (P¯+Q¯+R)(P¯+Q+R)(P+Q¯+R¯)
  3. P¯Q¯R+P¯QR+PQ¯R
  4. (P¯+Q¯+R)(P¯+Q+R)(P+Q¯+R)

Answer (Detailed Solution Below)

Option 3 : P¯Q¯R+P¯QR+PQ¯R
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Detailed Solution

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Fromthe given figure

GATE EC 2017 slot 2 part 2 D4

A = P̅ Q̅ R

B = P̅ Q R

C = P Q̅ R

F = A + B + C

= P̅ Q̅ R + P̅ Q R + P Q̅ R
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