1. Construct a truth table for the following: a) Xyz + x(yz)' + x'(y+z) + (xyz)' b) (x+y)(x'+z')(y +z) 2. Simplify the following functional expression and list the identity used at each srep. a) F(x,y,z) = y(x + (x+y)) b) F(x,y,z) = xyz + xz c) F(x,y, z) = (x' ty +z')+ xy + yz + xyz 3. Simplify the following function and show its identity, list the identity used at each step. a) z(w+x)' +wxz + wxyz' + wxyz b) y'(xz + xz) + z(x+y)' c) x(yz + x)(y' +z) 4. prove the following expression xy + xz + yz = xy + xz 5. Given the Boolean function, F(x, y, z)=xy + xyz a) expression for the complement of F. Express in Sum- of - Products form. b) Show that FF = 0 c) Show that F+F = 1