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The Consensus Theorem

The Consensus Theorem. XY + X’Z + YZ. XY + X’Z + YZ. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c'). Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’b + b’c’ + bc + cc’.

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The Consensus Theorem

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  1. The Consensus Theorem ECEn/CS 224

  2. XY + X’Z + YZ ECEn/CS 224

  3. XY + X’Z + YZ ECEn/CS 224

  4. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') ECEn/CS 224

  5. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’b + b’c’ + bc + cc’ ECEn/CS 224

  6. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’b + b’c’ + bc + cc’ ECEn/CS 224

  7. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’c’ + cb ECEn/CS 224

  8. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’c’ + bc = bc + a’b’d + a’cd + b’c’ + a’d’c + a’d’b’ ECEn/CS 224

  9. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b'+ c') +(b' + c) (b + c') = a’db’ + a’dc + a’d’b’ + a’d’c + b’c’ + bc = bc + a’db’ + a’dc + b’c’ + a’d’c + a’d’b’ XY ZX’ ZY YX ZX’ ZY ECEn/CS 224

  10. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’db’ + a’dc + a’d’b’ + a’d’c + b’c’ + cb = bc + a’db’ + a’dc + b’c’ + a’d’c + a’d’b’ XY ZX’ ZY YX ZX’ ZY ECEn/CS 224

  11. Problem 1: Simplify the expression a'd (b' + c) + a'd' (b’ + c') +(b' + c) (b + c') = a’b’d + a’cd + a’b’d’ + a’c’d’ + b’c’ + bc = bc + a’b’d + a’cd + b’c’ + a’b’d’ + a’c’d’ YX ZX’ ZY YX ZX’ ZY = bc + a’b’d + b’c’ + a’b’d’ YX ZX’ YX ZX’ ECEn/CS 224

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