Computer Science
Find the complement of F (a, b, c, d) using Demorgan's Laws. Show the relevant reasoning.
F(a, b, c, d)=a + {(b + c).(b' + d')}
Boolean Algebra
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Answer
[a + {(b + c).(b' + d')}]'
= a'.[{(b + c).(b' + d')}]' [De-Morgan's Law]
= a'.{(b + c)' + (b' + d')'} [De-Morgan's Law]
= a'.{(b'c') + (b''.d'')} [De-Morgan's Law]
= a'.{(b'c') + (bd)} [Involution Law: a''=a]
= a'b'c' + a'bd
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