Question

Помогите срочно (алгебра логики упростить) 1. (x+y)(¬x+y)(¬x+¬y) 2. ¬(x+y)(¬x+y)(¬x+¬y)

Answer 1

1. (x + y)(¬x + y)(¬x + ¬y) = (x¬x + ¬xy + xy + yy)(¬x + ¬y) =
= (0 + ¬xy + xy + y)(¬x + ¬y) = ¬x¬xy + ¬xxy + ¬xy + ¬xy¬y + xy¬y + y¬y =
= ¬xy + 0 + ¬xy + 0 + 0 + 0 = ¬xy + ¬xy = ¬xy

2. ¬(x + y)(¬x + y)(¬x + ¬y) = (¬x¬y)(¬x¬x + ¬xy + ¬x¬y + y¬y) =
= ¬x¬y(¬x + ¬xy + ¬x¬y + 0) = ¬x¬y¬x + ¬x¬y¬xy + ¬x¬y¬x¬y =
= ¬x¬y + 0 + ¬x¬y = ¬x¬y + ¬x¬y = ¬x¬y