Prove the following identity in a Boolean algebra, justifying each step by quoting one of the properties of a Boolean algebra:
(a + b)(a'c)' = a + bc'
(a + b)(a'c)' = a + bc'
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(a + b)(a'c)'
= (a + b)((a')' + c') <--[by DeMorgan's Law]
= (a + b)(a + c') <--[by Double Negation Law]
= a + bc' <--[by Distributive Law]
= (a + b)((a')' + c') <--[by DeMorgan's Law]
= (a + b)(a + c') <--[by Double Negation Law]
= a + bc' <--[by Distributive Law]