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Question Number 95860 by omere hum aFreeN last updated on 28/May/20

A^− ∙(B+B^− )∙(C+C^− )∙(D+D^− )

$$\overset{−} {{A}}\centerdot\left({B}+\overset{−} {{B}}\right)\centerdot\left({C}+\overset{−} {{C}}\right)\centerdot\left({D}+\overset{−} {{D}}\right) \\ $$

Answered by omere hum aFreeN last updated on 28/May/20

A^− B+A^− B^− ∙(C+C^− ) A^− BC+A^− BC^− +A^− B^− C+A^− B^− C^− ∙(D+D^− ) A^− BCD+A^− BCD^− +A^− BC^− D+A^− BC^− D^− +A^− B^− CD+A^− B^− CD^− +A^− B^− C^− D+A^− B^− C^− D^−

$$ \\ $$$$\overset{−} {{A}B}+\overset{−} {{A}}\overset{−} {{B}}\centerdot\left({C}+\overset{−} {{C}}\right) \\ $$$$\overset{−} {{A}BC}+\overset{−} {{A}B}\overset{−} {{C}}+\overset{−} {{A}}\overset{−} {{B}C}+\overset{−} {{A}}\overset{−} {{B}}\overset{−} {{C}}\centerdot\left({D}+\overset{−} {{D}}\right) \\ $$$$\overset{−} {{A}BCD}+\overset{−} {{A}BC}\overset{−} {{D}}+\overset{−} {{A}B}\overset{−} {{C}D}+\overset{−} {{A}B}\overset{−} {{C}}\overset{−} {{D}}+\overset{−} {{A}}\overset{−} {{B}CD}+\overset{−} {{A}}\overset{−} {{B}C}\overset{−} {{D}}+\overset{−} {{A}}\overset{−} {{B}}\overset{−} {{C}D}+\overset{−} {{A}}\overset{−} {{B}}\overset{−} {{C}}\overset{−} {{D}} \\ $$

Commented by prakash jain last updated on 28/May/20

B+B^− =1 So the given expression should simplify to A^−

$${B}+\overset{−} {{B}}=\mathrm{1} \\ $$$$\mathrm{So}\:\mathrm{the}\:\mathrm{given}\:\mathrm{expression}\:\mathrm{should} \\ $$$$\mathrm{simplify}\:\mathrm{to} \\ $$$$\overset{−} {{A}} \\ $$

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