Simplify-1-A-B-A-B-2-A-B-A-B-

Question Number 168858 by Shrinava last updated on 19/Apr/22

$$\mathrm{Simplify}: \\ $$$$\mathrm{1}.\:\left(\mathrm{A}\:+\:\mathrm{B}\right)\left(\mathrm{A}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\mathrm{2}.\:\left(\overline {\mathrm{A}}\:+\:\mathrm{B}\right)\left(\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}}\right) \\ $$

Answered by Rasheed.Sindhi last updated on 19/Apr/22

$$\mathrm{1}.\:\left(\mathrm{A}\:+\:\mathrm{B}\right)\left(\mathrm{A}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\:\:\:\:\:=\mathrm{AA}+\mathrm{A}\overline {\mathrm{B}}+\mathrm{BA}+\mathrm{B}\overline {\mathrm{B}} \\ $$$$\:\:\:\:\:=\mathrm{A}+\mathrm{A}\overline {\mathrm{B}}+\mathrm{AB}+\mathrm{0} \\ $$$$\:\:\:\:\:=\mathrm{A}+\mathrm{A}\left(\overline {\mathrm{B}}+\mathrm{B}\right) \\ $$$$\:\:\:\:\:=\mathrm{A}+\mathrm{A}\centerdot\mathrm{1} \\ $$$$\:\:\:\:\:=\mathrm{A}+\mathrm{A} \\ $$$$\:\:\:\:\:=\mathrm{A} \\ $$$$\mathrm{2}.\:\left(\overline {\mathrm{A}}\:+\:\mathrm{B}\right)\left(\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\:\:\:\:\:=\overline {\mathrm{A}}\overline {\mathrm{A}}+\overline {\mathrm{A}}\overline {\mathrm{B}}+\mathrm{B}\overline {\mathrm{A}}+\mathrm{B}\overline {\mathrm{B}} \\ $$$$\:\:\:\:\:=\overline {\mathrm{A}}+\overline {\mathrm{A}}\left(\overline {\mathrm{B}}+\mathrm{B}\right)+\mathrm{0} \\ $$$$\:\:\:\:\:=\overline {\mathrm{A}}+\overline {\mathrm{A}}\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:=\overline {\mathrm{A}}+\overline {\mathrm{A}} \\ $$$$\:\:\:\:\:=\overline {\mathrm{A}} \\ $$

Commented by Shrinava last updated on 19/Apr/22

$$\mathrm{perfect}\:\mathrm{thankyou}\:\boldsymbol{\mathrm{sir}} \\ $$

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