8. Prove the identity of each of the following Boolean equations, using algebraic manipulation: a). AB+BC + AB + BC-1 9. Simplify the Boolean expression to an expression containing a minimum number of literals: ABD+ ACD+BD 10. Find the complement of the following expression: (A+ B + C)(AB + )(A+ BC) 11. Optimize the following Boolean functions by means of a three-variable map: a).F(A,B,C)-m(0,2,3,4,5.7) b), F(A,B,C)- + AC + BC + 12. Optimize the following Boolean functions by means of a four-variable map: a).F(A,B,C,D)-5%10,2378.10,l213) b).FCA,B,C,D)-BD + ABD+ 13. Optimize the Boolean function by finding all prime implicants and essential prime implicants and applying the selection rule: FOW,X,Y,z)-m(0,2,4,6,789121315)