Problem 5 Use Boolean algebra (i.e., do not exhaustively prove using a truth table) to show whether the given equations are true. You must label each theorem or postulate with either its name or number. For reference, a table of all theorems and postulates is provided below. + C + (int: + : 8) AB : T8) 1. 2. AB + CD + BCD = AB + CD(Hint: + B = AB : T8) 3. AB + BC + C + BC = ABC + AB + C Expression a + 0 = a Dual P2 a 1 = a a + b = b + a a + (b + c) = (a + b) + c a + bc = (a + b)(a + c) ab = ba P3 a(bc) = a(b + c) = ab + ac a = 0 = (ab)c P4 P5 P6 a + = 1 T1 a + a = a a a = a T2 a 0 = 0 a + 1 = 1 T3 a + ab a + b = a +b ab + ab = a a(a + b) = a a( + b) = ab (a + b)(a + b) T4 T5 T6 ab + abc (a + b)(a + b + c) = (a + b)(a + c) ab + ac T7 a + b = b ab + c + bc = ab + c ab = + b T8 (a + b)( + c)(b + c) f (x1,x2, ..., Xn) = x1(f (1, x2, ...,Xn) + X1f (0,x2,..., Xn) ) = (a + b)+ c) T9 T10(a) T10(b) f(x1,X2, ..., Xn) = [x1 + f(0, x2, ..., xn)]+ f(1,x2, ...,Xn)]