I. BOOLEAN'S ALGEBRA

1. X        = ABC + A/C   

               = C(AB + A/)

               = C(A/ + B)

              

       2. Y         = (Q + R)(Q/ + R/)

               = QQ/ + QR/ + RQ/ + RR/

               = QR/ + Q/R

       3. W        = ABC + AB/C + A/

               = AC(B + B/) + A/

      = AC + A/

               = A/ + C

       4. Q        = (RST)/(R + S + T)/

               = (R/ + S/ + T/)(R/S/T/)

               = R/S/T/ + R/S/T/ + R/S/T/

               = R/S/T/

       5. X        = A/B/C/ + A/BC + ABC + AB/C/ + AB/C

       = A/B/C/ + AB/C/ + A/BC + ABC + AB/C

               = B/C/(A/ + A) + BC(A/ + A) + AB/C

               = B/C/ + BC + AB/C

= B/C/ + C(B + A.B/)
= B/C/ + C(B + A)
= B/C/ + BC + A.C

               = B/C/ + C(A + B)

       6. Z         = (B + C/)(B/ + C) + (A/ + B + C)/

               = BB/ + BC + B/C/ + CC/ + (A//B/C//)

               = BC + B/C/ + AB/C

               = BC + B/(C/ + AC)

               = BC + B/(C/ + A)

               = BC + B/C/ + B/A

       7. Y         = (C + D)/ + A/C D/ + AB/C/ + A/B/CD + ACD/

               = C/D/ + A/CD/ + ACD/ + AB/C/ + A/B/CD

               = C/D/ + CD/(A/ + A) + AB/C/ + A/B/CD

               = C/D/ + CD/ + AB/C/ + A/B/CD

               = D/(C/ + C) + AB/C/ + A/B/CD

               = D/ + AB/C/ + A/B/CD

               = D/ + B/(AC/ + A/CD)

       8. X         = AB(C/D)/ + A/BD + B/C/D/

               = AB(C + D/) + A/BD + B/C/D/

               = ABC + ABD/ + A/BD + B/C/D/

               = ABC + A/BD + ABD/ + B/C/D/

               = B(AC + A/D) + D/(AB + B/C/)