23. Use the properties and theorems of Boolean algebra to reduce the following expressions to OR-AND expressions. The expressions may not be unique. Construct the truth table, which will be unique, by inspection of your final expression.

(a) a′b + ab′

*

(b) ab + a′b′

(c) ab + ab′ + a′b

(d) ((ab ⊕ b′)′ + ab)′

(e) (a′bc + a)b

(f) (ab′c)′(ac)′

(g) (a ⊕

b) ⊕ c

(h) a ⊕ (b ⊕ c)

(i) ((a + b)(a′ + c)(b′ + c′))′

(j) (a + b)′ + c