Solution steps may not be identical to key. But they must follow the
boolean rules correctly.

Part 2

a*(a+b)=
  distribution
aa+ab=
  itempotent
a+ab=
  identity
a1+ab=
  distribution
a(1+b)=
  null
a(1)=
  identity
a

Part 3

a. a*b*c+d*e+e=
  identity
a*b*c+d*e+1*e=
  distribution
a*b*c+(d+1)*e=
  null
a*b*c+1*e=
  identity
a*b*c+e

b. a*(b+a+c)=
  distribution
a*b+a*a+a*c=
  itempotent
a*b+a+a*c=
  identity
a*b+a*1+a*c=
  distribution
a*(b+1+c)=
  null
a*(1)=
  identity
a

c. (a*b+c+d*e)*e*d=
  distribution
a*b*d*e+c*d*e+d*e*d*e=
  itempotent
a*b*d*e+c*d*e+d*e=
  identity
a*b*d*e+c*d*e+1*d*e=
  distribution
(a*b+c+1)*d*e=
  null
(1)*d*e=
  identity
d*e

d. !(!d*!d*e)=
  itempotent
!(!d*e)=
  deMorgan
!!d+!e=
  cancellation
d+!e

e. c*(a+b+!(!c+!d))*d=
  deMorgan
c*(a+b+!!c*!!d)*d=
  null
c*(a+b+c*d)*d=
  distribution
c*d*a+c*d*b+c*d*c*d=
  itempotent
c*d*a+c*d*b+c*d=
  identity
c*d*a+c*d*b+c*d*1=
  distribution
c*d*(a+b+1)=
  null
c*d*(1)=
  identity
c*d

f. (a*c+b+d)*b=
  distribution
a*c*b+b*b+d*b=
  itempotent
a*c*b+b+d*b=
  identity
a*c*b+1*b+d*b=
  distribution
(a*c+1+d)*b=
  null
(1)*b=
  identity
b

g. a*c+c*(!a+a*b)=
  distribution
(a+!a+a*b)*c=
  inverse
(1+a*b)*c=
  null
(1)c=
  identity
c

h. (a+b*c*d+e)*e*d=
  distribution
a*e*d+c*d*e*d+e*e*d=
  itempotent
a*e*d+c*e*d+e*d=
  identity
a*e*d+c*e*d+1*e*d=
  distribution
(a+c+1)*e*d=
  null
(1)*e*d=
  identity
e*d

Part 4

a. a+!a+b=
  inverse
1+b=
  null
1

b. a*(!a+b)=
  distribution
a*!a+a*b=
  inverse
0+a*b=
  identity
a*b

c. !a+a*b=
  cancelation
!a+!!(a*b)=
  deMorgan
!a+!(!a+!b)=
  deMorgan
!(a*(!a+!b))=
  distribution
!(a*!a+a*!b)=
  inverse
!(0+a*!b)=
  null
!(a*!b)=
  deMorgan
!a+!!b=
  cancellation
!a+b

d. !a+a*!b=
  cancellatiion
!a+!!(a*!b)=
  deMorgan
!a+!(!a+!!b)=
  inverse
!a+!(!a+b)=
  deMorgan
!(a*(!a+b))=
  distribution
!(a*!a+a*b)=
  inverse
!(0+a*b)=
  identity
!(a*b)

e. a*(!a*b)=
  associative
(a*!a)*b=
  inverse
0*b=
  null
0

f. !a*(a+!b)=
  distribution
!a*a+!a*!b=
  inverse
0+!a*!b=
  identity
!a*!b=
!(a+b)