Question

what would be the complement of (ab+ac)
hint- (apply DeMorgan's law)

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Answer 1

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TO DETERMINE

In Boolean Algebra the complement of ( a.b + a.c )

PROPERTY TO BE IMPLEMENTED

1. DISTRIBUTIVE PROPERTY

$\sf{a.(b + c) = a.b + a.c \: }$

2. DE MORGAN'S LAW

$\sf{(i) \: \: \: \: (a.b) '=a' + \: b'}$

$\sf{(ii) \: \: \: \: (a+b) '=a'. \: b'}$

CALCULATION

$\sf{The \: complement \: of \: \: ( a.b + a.c )}$

$= \sf{ ( a.b + a.c ) ' \: }$

$= \sf{[ \: a.(b +c ) \: ] '} \: \: \: ( \: using \: property \: 1 \: )$

$= \sf{[ \: a ' + (b +c ) '} \: ]\: \: ( \: using \: property \: 2(i)\: )$

$= \sf{ \: a ' + ( \: b' .c ' \: )} \: \: \: ( \: using \: property \: 2(ii)\: )$

RESULT

$\boxed{ \sf{ \: \: \: ( a.b + a.c ) ' \: = \: a ' + ( \: b' .c ' \: ) \: \: \: }}$

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LEARN MORE FROM BRAINLY

If A, B and C are any three sets then prove the following using venn-diagram.

A∩(BUC) = (A∩B) U (A∩C)

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Answer 2

Answer:

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