The following propositional statement is equal to ((A → B) → C) → ((A → C) → B)

(A) (B → C)
(B) (B → C\’)
(C) (B\’ → C\’)
(D) (B\’ → C)


Answer: (C)

Explanation: Let’s solve it
((A → B) → C) → ((A → C) → B)
=> ((A’ + B)’ + C)’ + ((A’ + C)’ + B ) (we know A → B = A’ + B)
=> ((AB’) + C)’ + AC’ + B
=> (AB’)’C’ + AC’ + B
=> (A’ + B)C’ + AC’ + B
=> A’C’ + BC’ + AC’ + B
=> (A + A’)C’ + (1 + C’)B
=> C’ + B (A + A’ = 1 and 1 + C’ = 1)
=> (B’ → C’)


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