21. Use the properties and theorems of Boolean algebra to reduce the following expressions to AND-OR expressions without parentheses. The expressions may not be unique. Construct the truth table, which will be unique, by inspection of your final expression.

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(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)′