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In each case, multiply out to obtain a sum of products:(Simplify where possible) (a) (M' + N' + O + P')(O + P + M
In each case, multiply out to obtain a sum of products:(Simplify where possible) (a) (M' + N' + O + P')(O + P + M + N)(P + N + O)(O + M')(M + P) (b) (A + B + C)(A + D' + C')(C' + A' + D)(B' + A')(D' + A) (a) Reduce to a minimum sum of products(4 terms): (b) Reduce to a minimum sum of products (3 terms):(consensus theorem) (AB') + (A + B)(C D) (C) Reduce to a minimum product of sums (4 terms):(consensus theorem) (A + B + C')(A + B + E)(A + E + D')(A + B + D)(A' + C) Eliminate the exclusive-OR, and then factor to obtain a minimum product of sums: (a) A'B + (A CD) (b) AB + (C B')A' + C'B
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