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Question

# The equivalent expression for the following Boolean expression is/are F(A,B,C,D)=BÂ¯Â¯Â¯Â¯Â¯D+Â¯Â¯Â¯Â¯BCD+ABC+ABÂ¯Â¯Â¯Â¯CD+Â¯Â¯Â¯Â¯B Â¯Â¯Â¯Â¯Â¯D

A

F=¯¯¯¯¯D+¯¯¯¯BCD+ABC+AB¯¯¯¯CD

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B

F=¯¯¯¯¯D+(BC+AB)D+ABC

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C

F=¯¯¯¯¯D+¯¯¯¯BC+AB

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D

F=¯¯¯¯¯D+¯¯¯¯BC+AB

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Solution

## The correct option is D F=¯¯¯¯¯D+¯¯¯¯BC+AB F=D+(B+¯¯¯¯B)+¯¯¯¯BCD+ABC+AB¯¯¯¯CD =¯¯¯¯¯D+¯¯¯¯BCD+ABC+AB¯¯¯¯CD =¯¯¯¯¯D+¯¯¯¯BCD+AB(C+¯¯¯¯CD) =¯¯¯¯¯D+¯¯¯¯BCD+AB(C+D) =¯¯¯¯¯D+(¯¯¯¯BC+AB)+ABC =(¯¯¯¯¯D+D)(¯¯¯¯¯D+¯¯¯¯BC+AB)+ABC F=¯¯¯¯¯D+¯¯¯¯BC+AB

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