Bolean Algebra

a. X     = ABC + A/C

    = C(AB + A/)

b. Y     = (Q+R)(Q/+R/)

    = QQ/ + Q/R/ + RQ + RR/
    = QR/ + RQ/

C. W    = ABC + AB/C + A/

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

d. Q    = (RST)/ (R+S+T)/

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

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

    = B/C/ (A/+A) + BC(A/+A) +AB/C
    = B/C/ + BC + AB/C
    = 1 + AB/C

f. Z    = (B+C/)(B/+C) + (A/+B+C/)/

    = BB/ + BC +C/B/ + C/C + (A/+B+C/)/
    = 1 + (A/+B+C/)/
    = 1 + A// B/ C//
    = 1 + A B/ C
    = 1

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

    = C/D/ + A/CD/ + AB/C/ + A/B/CD + ACD/
    = D/(C/+A/C+AC) b/(AC/+A/CD)
    = D/(C/+C) + B
    = D/+B

h. X     = AB(C/D)/ + A/BD + B/C/D/

    = AB(C//D/) + A/BD + B/C/D/
    = ABCD/ +A/BD + B/C/D/
    = A/BD + D/(ABC+B/C/)
    = A/BD + D/((A+B/C/)(B+B/C/)(C+B/C/))
    = A/BD + D/((A+B/)(A+C/)(B+B/)(B+C/)(C+B/)(C+C/)
    = A/BD + D/(AA+AC/+B/A+B/C+BC+BB+CC/+C/B)
    = A/BD + D/(A+AC/+B/A+B/C/+BC+C/B
    = A/BD + D/(A+B/C/+BC+C/B
    = A/BD + D/(A+B+C/)
    = A/BD + DA + DB + DC/
    = D(A/D+A) + DB + DC/
    = D(A+D) + DB + DC/
    = DA + D + DB + DC/
    = A + D(B+C/)