Question

Упростите логические выражения
1) (A&B) v (ᾹvB) v (C&B)=
2) (A&B̅) v (A&B) v (A&C̅)=
3) (A&B) v (A&B̅) v (Ᾱ&C)=

Answer 1

1)упрощениеAB+(!A+B)+CB -> !A+B
таблица истинности
A B C   F0 0 0 = 10 0 1 = 10 1 0 = 10 1 1 = 11 0 0 = 01 0 1 = 01 1 0 = 11 1 1 = 1
2)упрощениеA!B + AB + A!C -> A(!B + B + !C) !B+B+!C -> 1A(!B+B+!C) -> A
таблица истинности
A B C   F0 0 0 = 00 0 1 = 00 1 0 = 00 1 1 = 01 0 0 = 11 0 1 = 11 1 0 = 11 1 1 = 1
3)упрощениеAB+A!B+(!A+C) -> B+!B+!A+CB+!B+!A+C -> 1
таблица истинности
A B C   F0 0 0 = 10 0 1 = 10 1 0 = 10 1 1 = 11 0 0 = 11 0 1 = 11 1 0 = 11 1 1 = 1