what would be the complement of (ab+ac)
hint- (apply DeMorgan's law)
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what would be the complement of (ab+ac)
hint- (apply DeMorgan's law)
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[tex]\displaystyle\huge\red{\underline{\underline{Solution}}}[/tex]
TO DETERMINE
In Boolean Algebra the complement of ( a.b + a.c )
PROPERTY TO BE IMPLEMENTED
1. DISTRIBUTIVE PROPERTY
[tex] \sf{a.(b + c) = a.b + a.c \: }[/tex]
2. DE MORGAN'S LAW
[tex] \sf{(i) \: \: \: \: (a.b) '=a' + \: b'}[/tex]
[tex] \sf{(ii) \: \: \: \: (a+b) '=a'. \: b'}[/tex]
CALCULATION
[tex] \sf{The \: complement \: of \: \: ( a.b + a.c )} [/tex]
[tex] = \sf{ ( a.b + a.c ) ' \: }[/tex]
[tex] = \sf{[ \: a.(b +c ) \: ] '} \: \: \: ( \: using \: property \: 1 \: )[/tex]
[tex] = \sf{[ \: a ' + (b +c ) '} \: ]\: \: ( \: using \: property \: 2(i)\: )[/tex]
[tex] = \sf{ \: a ' + ( \: b' .c ' \: )} \: \: \: ( \: using \: property \: 2(ii)\: )[/tex]
RESULT
[tex] \boxed{ \sf{ \: \: \: ( a.b + a.c ) ' \: = \: a ' + ( \: b' .c ' \: ) \: \: \: }}[/tex]
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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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