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

$$\mathrm{Simplify}:$$$$1.(\mathrm{A}+\mathrm{B})(\mathrm{A}+\bar{\mathrm{B}})$$$$2.(\bar{\mathrm{A}}+\mathrm{B})(\bar{\mathrm{A}}+\bar{\mathrm{B}})$$

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

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

Commented by Shrinava last updated on 19/Apr/22

$$\mathrm{perfect}\mathrm{thankyou}\mathbf{sir}$$

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