Simplify as much as possible.

1. $(AB + C) (AB + C')$
   $=AB(C+C')$ (distributive law (16))
   $=AB(1)$ (identity 7)
   $=AB$ (identity 2)
   A \& B

2. $X'W + XW' + XW + X'W'$
   $=X'W'+X'W+XW'+XW$ (commutative law (10))
   $=X'(W'+W)+X(W'+W)$ (distributive law)
   $=(X'+X)(W'+W)$ (distributive law)
   $=1\cdot1$ (identity 7)
   $=1$ (identity 3)
3. $pqr + rp$
   $=p(qr+r)$ (distributive)
   $=p(q+1)r$ (distributive)
   $=pr$ (identity 3)
   p \& r

4. $(y'+z')xyz$
   $=xyy'z+xyzz'$ (distributive)
   $=0+0=0$ (identity 8)
5. $(C+DX) (C+EX)$
   $=C+(DX)(EX)$ (distributive law (15))
   $=C+DEX$ (identity 6)
   C | (D \& E \& X)
6. $T(L'+V) + TV'$
   $=T(L'+V+V')$ (distributive law)
   $=T(L'+1)=T$ (identities 7 and 3)
7. $fg \oplus 1$
   $=0fg+1(fg)'$ (definition)
   $=f'+g'$ (DeMorgan's law)
   ~f | ~g

8. $(m \oplus n) \oplus (m' \oplus n)$
   $=(m \oplus m') \oplus (n \oplus n)$ (XOR is commutative & associative)
   $=1 \oplus 0=1$ (identities)
9. $(uw \oplus (t+u))'$
   $=((uw)'(t+u)+uw(t+u)')'$ (definition)
   $=((u'+w')(t+u)+uu'wt)'$ (DeMorgan's)
   $=(u'+w')'+(t+u)'$ (identities & DeMorgan's)
   $=uw+t'u'$ (DeMorgan's once again)
   u \& w | ~t \& ~u
10. $(xy+z)'(z(x'+y'))$
    $=z'(xy)'z(x'+y')=0$ (DeMorgan's and identity)
11. $[(x+a)(x+b)(x+c)(x+d)]'$
    $=(x+abcd)'=x'(abcd)'$ (Distributive & DeMorgan's)
    ~x \& ~(a \& b \& c \& d)