$($i$)$ Prove that the Dual of the XOR is also its complement. $(20$pts$.)$

$($ii$)$ Prove or Dis$-$prove the following relationships. Use any method.

Show your work. $(20$pts$.)$

a$.x^{\text{'}}o+1=x^{\text{'}}$

b$.x(Yo+Z)=$xYo$+YZ$

c$.(x+Y)o+(x+Z)=x(Yo+Z)$

d$.A^{\text{'}}o+Bo+Co+D=A^{\text{'}}o+Bo+C^{\text{'}}o+D^{\text{'}}$