I want to simplify this logic expression:
Y = (A ∧ B ∧ ¬C ∧ D ) ∨ (C ∧ ¬D) ∨ (A ∧ B ∧ C) ∨ (¬A ∧ C)
I know it must become Y = (A ∧ B ∧ D) ∨ (C ∧ ¬D) ∨ (¬A ∧ C) and I found it with Karnaugh, but I can't find it with boolean simplification. I arrive here:
Y = (A ∧ B ∧ C) ∨ (A ∧ B ∧ D) ∨ (¬A ∧ C) ∨ (C ∧ ¬D)
Can anyone help me with this, explaining me how to arrive to the solution? Thanks!
$(A \land B \land C) \lor (A \land B \land D) $
can be simplified to
$A \land B \land (C \lor D) $
which can be rewritten as:
$A\land B\land ((C\land D)\lor(C\land \lnot D) \lor (\lnot C \land D))$
Notice that $C \land \lnot D$ appears later in Y, so we ignore that term (since Y would then be true anyway):
$A\land B \land ((C\land D) \lor (\lnot C\land D))$
which finally simplifies to
$A \land B \land D$