Question #134596
Simplify (a’ * b’ * c) + (a * b’ * c) + (a * b’ * c’)
1
Expert's answer
2020-09-28T09:03:24-0400

(¬ A∧¬ B∧ C)+(A∧¬ B∧ C)+(A∧¬ B∧¬ C)=(¬ B∧ C∧ A)∨(¬ B∧ C∧¬ A)∨(A∧¬ B∧¬ C)=(¬ B∧ C∧ A)∨(¬ B∧ C∧¬ A)∨(A∧¬ B∧¬ C)=((¬ B∧ C)∨ A)∧((¬ B∧ C)∨¬ B)∧((¬ B∧ C)∨¬ C)=((¬ B∧ C)∨ A)∧(¬ B∨(¬ B∧ C))∧((¬ B∧ C)∨¬ C)=((¬ B∧ C)∨ A)∧(¬ B∨(¬ B∧ C))∧((¬ B∧ C)∨¬ C)=(A∨(¬ B∧ C))∧¬ B∧((¬ B∧ C)∨¬ C)=(A∨(¬ B∧ C))∧¬ B∧((¬ B∧ C)∨¬ C)=(A∨¬ B)∧(A∨ C)∧¬ B∧((¬ B∧ C)∨¬ C)=(A∨¬ B)∧(A∨ C)∧¬ B∧((¬ B∧ C)∨¬ C)=(A∨¬ B)∧(A∨ C)∧¬ B∧((¬ B∧ C)∨¬ C)=¬ B∧(A∨ C)∧(¬ C∨(¬ B∧ C))=¬ B∧(A∨ C)∧((¬ C∨¬ B)∧(¬ C∨ C))=¬ B∧(A∨ C)∧((¬ C∨¬ B)∧(¬ C∨ C))=¬ B∧(A∨ C)∧(¬ C∨¬ B)=¬ B∧(¬ B∨¬ C)∧(A∨ C)=¬ B∧(A∨ C)\left(\neg \:A\wedge \neg \:B\wedge \:C\right)+\left(A\wedge \neg \:B\wedge \:C\right)+\left(A\wedge \neg \:B\wedge \neg \:C\right)=\left(\neg \:B\wedge \:C\wedge \:A\right)\vee \left(\neg \:B\wedge \:C\wedge \neg \:A\right)\vee \left(A\wedge \neg \:B\wedge \neg \:C\right)=\left(\neg \:B\wedge \:C\wedge \:A\right)\vee \left(\neg \:B\wedge \:C\wedge \neg \:A\right)\vee \left(A\wedge \neg \:B\wedge \neg \:C\right)=\left(\left(\neg \:B\wedge \:C\right)\vee \:A\right)\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:B\right)\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(\left(\neg \:B\wedge \:C\right)\vee \:A\right)\wedge \left(\neg \:B\vee \left(\neg \:B\wedge \:C\right)\right)\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(\left(\neg \:B\wedge \:C\right)\vee \:A\right)\wedge \left(\neg \:B\vee \left(\neg \:B\wedge \:C\right)\right)\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(A\vee \left(\neg \:B\wedge \:C\right)\right)\wedge \neg \:B\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(A\vee \left(\neg \:B\wedge \:C\right)\right)\wedge \neg \:B\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(A\vee \neg \:B\right)\wedge \left(A\vee \:C\right)\wedge \neg \:B\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(A\vee \neg \:B\right)\wedge \left(A\vee \:C\right)\wedge \neg \:B\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\left(A\vee \neg \:B\right)\wedge \left(A\vee \:C\right)\wedge \neg \:B\wedge \left(\left(\neg \:B\wedge \:C\right)\vee \neg \:C\right)=\neg \:B\wedge \left(A\vee \:C\right)\wedge \left(\neg \:C\vee \left(\neg \:B\wedge \:C\right)\right)=\neg \:B\wedge \left(A\vee \:C\right)\wedge \left(\left(\neg \:C\vee \neg \:B\right)\wedge \left(\neg \:C\vee \:C\right)\right)=\neg \:B\wedge \left(A\vee \:C\right)\wedge \left(\left(\neg \:C\vee \neg \:B\right)\wedge \left(\neg \:C\vee \:C\right)\right)=\neg \:B\wedge \left(A\vee \:C\right)\wedge \left(\neg \:C\vee \neg \:B\right)=\neg \:B\wedge \left(\neg \:B\vee \neg \:C\right)\wedge \left(A\vee \:C\right)=\neg \:B\wedge \left(A\vee \:C\right)


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