Question

Найдите значения логических выражений: a) F = (0 v 0) v (1 v 1) b) F = (1 v 1) v (1 v 0) c) F = (0 & 0) & (1 & 1) d) F = (1 & 0) v (¬1 & ¬0) e) F = ¬(1 & 0) f) F = 1 v (1 & 0) g) F = ¬1 v ¬0 h) F = (1 v ¬0) & 0 i) F = 1 & 0 v 1 j) F = (1 v 0) & (¬1 v ¬0)

Answer 1

ответ

a)F=(0 v 0) v (1 v 1)

Answer 2

a) F = (0 v 0) v (1 v 1) = 0 v 1 (applying the rule A v A = A and A v 1 = 1) = 1 (applying the rule A v 1 = 1)

b) F = (1 v 1) v (1 v 0) = 1 v 1 (applying the rule A v A = A) = 1 (applying the rule A v 1 = 1)

c) F = (0 & 0) & (1 & 1) = 0 & 1 (applying the rule A & A = A and A & 0 = 0) = 0 (applying the rule 0 & A = 0)

d) F = (1 & 0) v (¬1 & ¬0) = 0 v ¬1 (applying the rule A & ¬A = 0) = 0 (applying the rule 0 v A = A)

e) F = ¬(1 & 0) = ¬0 (applying the rule A & 0 = 0) = 1 (applying the rule ¬0 = 1)

f) F = 1 v (1 & 0) = 1 (applying the rule A v 1 = 1)

g) F = ¬1 v ¬0 = 0 v 1 (applying the rule ¬A = 1 if A = 0 and ¬A = 0 if A = 1) = 1 (applying the rule 0 v A = A)

h) F = (1 v ¬0) & 0 = 1 & 0 (applying the rule A v ¬A = 1 and A & 0 = 0) = 0 (applying the rule 0 & A = 0)

i) F = 1 & 0 v 1 = 0 v 1 (applying the rule A & 0 = 0 and A v 1 = 1) = 1 (applying the rule 0 v A = A)

j) F = (1 v 0) & (¬1 v ¬0) = 1 & 1 (applying the rule A v ¬A = 1 and A & ¬A = 0) = 1 (applying the rule A & 1 = A)