7. Boolean Algebra (10 points) Prove that (A.B+(A'+B').(C'+D).(C.D.1+A.B)-A.B using fewer than 7 applications of Boolean Algebra axioms and theorems, not counting applications of associativity (11a,b) and commutivity (10a,b). Show all steps and write down the axiom/theorem number for each step Hint: Start with two applications of De Morgan's Theorem 10a: 10b: 1a: 0.0=0 1b: 1+1=1 2a: 1.1=1 2b: 0+0=0 3a: 0.1 = 1.0=0 3b: 1 +0 = 0+1 = 1 4a: If x=0, then x' = 1 4b: If x=1, then x'-0 5a: x.0 = 0 5b: x+1=1 x.y=y.x x+y=y+x lib: 12a: 12b: 13a: 13b: xt(ytz)=(x+y)+z x.(y+z) = xy + xz xty.z= (x+y)(x+z) xtx.y-x x.(x+y)=x 15a: 15b: 16a: (xy)'= x'+y, (x+y)'=x'y' x+x',y=x+y 6b: x+0=x 7b: x+x=x 8a: xx'=0 9: (x), = x