Need help with Boolean algebra. 3.8, 3.10a, 3.12, 3.14e

.) Factor to obtain a product of sums. (Stmplity where possible.) (a) BCD + C'D'+ B'CD +CL (b) A'CD ABD' + A'CD+ B'D 3.8 Write an expression for F and simplify. 3.9 lsthe following distributive law valid? A $BC (A BOA ed) Prove your answer 3.10 (a) Reduce to a minimum sum of products (three terms): (b) Reduce to a minimum sum of products (four terms): (c) Reduce to a minimum product of sums (three terms): (A BC) + BD + ACD Boolean Algebra (Continued) 83 3.11 Simplify algebraically to a minimum sum of products (ive terms): (A B' C+E(A+ B'+D+ E)(B +C+D+E) 3.12 Prove algcbraically that the following equation is valid: ACD'E +A'B'D + ABCE + ABD A'B'D'+ABD+BCD'E Simplify each of the following expressions: (a) KLMN' + K'L'MN MN (b) KI'M' +MN' +LM'N 3.13 (d) (K'+ L M'+N(K'+MN+R(K' + M'+ N + R)KM 3.14 Factor to obtain a product of sums: (a) K'L'M + KM'N + KIM +LM'N (lour terms) (b) KI. + K'L' + L'M'N' + LMN lour terms) (c) KI. + K'I'M + L'M'N + L.M'N' (four terms) (d) K'M'N+ KI'N'+ K'MN+LN (four terms) (e) WXY+ WX'Y+ WYz+ XYZ (three terms) 3.15 Multiply out to oblain a sum of products (a) (k' + M'+ N)(K'+ M)(. +M+N(K' + L M)(M + N) (three terms)