Prove or Disprove the following expressions

1. $(X \oplus Y)' = (X' \oplus Y)$
   $X' \oplus Y = X'Y' + XY = ((X+Y)(X'+Y'))' = (X \oplus Y)'$
   True
2. $(A' \oplus T')= ( A \oplus T)$
   $A' \oplus T' = A''T'+A'T'' = AT' + A'T = A \oplus T$
   True
3. $[a'(b + c')]' + b'c = a$
   $[a'(b+c')]' + b'c = a + b'c + b'c = a + b'c$
   False: let $a=0$, $b=0$, $c=1$
4. $wvx'+wv'x+w'vx' + w'v'x = w\oplus v \oplus x$
   $wvx'+wv'x+w'vx'+w'v'x = w(vx'+v'x)+w'(vx'+v'x) = v \oplus x$
   False: let $w=v=x=1$
5. $(A+D) (A + B + D) = (A+ B)$
   $(A+D)(A+B+D) = (A+D)((A+D)+B) = A+D$
   False: let $A=0$, $B=1$, $D=0$
6. $(M'N) \oplus (MN')= M \oplus N$
   $M'N\oplus MN' = M'N(M'+N) + MN'(M+N') = M'N + MN'$
   True
7. $(x+a)(y+b)(x+c)(y+a)(x+b)(y+c) = (xy + abc)$
   $(x+a)(x+b)(x+c)(y+a)(y+b)(y+c)=(x+abc)(y+abc)=xy+abc$
   True
8. $(K \oplus L \oplus M \oplus N \oplus P)' = (K' \oplus L' \oplus M' \oplus N'\oplus P')$
   $((K\oplus L)\oplus(M\oplus N)\oplus P)'=(K'\oplus L'\oplus M'\oplus N'\oplus P)'=K'\oplus L'\oplus M'\oplus N'\oplus P'$
   True