NIMCET 2017 Question Paper with solutions

Question : 23 of 120

Marks: +1, -0

Which term is reductant in the expression AB + A'C + BC?

Solution:

The Correct Answer is

A B+A^{'} C

The simplification of the boolean expression:

A B+A^{'} C+B C=

\;\; = {AB}+ {A}^{'} {C}+ {BC} {⋆} 1\{ {as} {A} {⋆} 1= {A}\}

\;\; = {AB}+ {A}^{'} {C}+ {BC}( {A}+ {A}^{'})\{\;\text " as Complement law: "\; {A}+ {A}^{'}=1\}

\;\; = {AB}+ {A}^{'} {C}+ {ABC}+ {A}^{'} {BC}\{ {as} \;\text " Absorption law: "\; {A}( {B}+ {C})= {AB}+ {BC} {AB}= {BA}\}

\;\; = {AB}+ {ABC}+ {A}^{'} {C}+ {A}^{'} {CB}\{\;\text " as Commutative Law: "\; {A}+ {B}= {B}+ {A} {AB}= {BA}\}

\;\; = {AB} {⋆} 1+ {ABC}+ {A}^{'} {C} {⋆} 1+ {A}^{'} {CB}\{ {as} {A} {⋆} 1= {A}\}

\;\; = {AB}(1+ {C})+ {A}^{'} {C}(1+ {B})\{ {as} {AB}+ {BC}= {A}( {B}+ {C})\}

\;\; = {AB} {⋆} 1+ {A}^{'} {C} {⋆} 1\{ {as} 1+ {A}=1\}

\;\; = {AB}+ {A}^{'} {C}\{ {as} {A} {⋆} 1= {A}\}

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