Simplify the following expressions using boolean algebra

a)        x   = ABC + A/C

= C ( AB + A/ )

= C ( B + A/ )

= A/C + BC

b)        y   = ( Q + R )( Q/ + R/ )

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

= QR/ + Q/R

c)        w  =  ABC + AB/C + A/

= AC ( B+B/ ) + A/

= AC + A/

d)       q   = R/S/T/ (R + S + T)/
     = (RST)/ (R + S + T)/
     = (RST)/ + (RST)/ +(RST)/
     = (RST)/

e)        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 + A.B/.C

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

f)         z   = ( B + C/)(B/ + C) + A// + B/ + C//

= BB/ + BC + B/C/ + CC/ + AB/C

= BC + B/C/ + AB/C

= BC + B/ (C/ + AC)

= BC + B/ (C/ + A)

= BC + B/C/ + AB/

g)        y   = (C + D)/ + A/CD/ + 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)

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

= AB (CD/) + 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/)