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Answer to Question #134596 in Discrete Mathematics for vikas

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

"\\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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