(a) A + B = B + A
A | B | A+B | B+A |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 |
(b) A B = B A
A | B | A B | B A |
0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
T2. Hukum Asosiatif
(a) (A + B) + C = A + (B + C)
A | B | C | A+B | (A+B)+C | B+C | A+(B+C) |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
(b) (A B) C = A (B C)
A | B | C | A B | (A B) C | B C | A (B C) |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
(a) A (B + C) = A B + A
A | B | C | B+C | A(B+C) | A B | AB+A |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
(b) A + (B C) = (A + B) (A + C)
A | B | C | B C | A+(BC) | A+B | A+C | (A+B)(A+C) |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
(a) A + A = A
A | A+A |
0 | 0 |
1 | 1 |
(b) A A = A
A | AA |
0 | 0 |
1 | 1 |
T5.
(a) AB + AB’ = A
A | B | B’ | A B | A B’ | AB+AB’ |
0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 |
(b) (A+B) (A+B’) = A
A | B | B’ | A+B | A+B’ | (A+B)(A+B’) |
0 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
T6. Hukum Redudansi
(a) A + A B = A
A | B | A B | A+AB |
0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 |
(b) A (A + B) = A
A | B | A+B | A(A+B) |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 |
T7.
(a) 0 + A = A
A |
| 0+A |
0 | 0 | 0 |
1 | 0 | 1 |
(b) 0 A = 0
A |
| 0 A |
0 | 0 | 0 |
1 | 0 | 0 |
T8.
(a) 1 + A = 1
A |
| 1+A |
0 | 1 | 1 |
1 | 1 | 1 |
(b) 1 A = A
A |
| 1 A |
0 | 1 | 0 |
1 | 1 | 1 |
T9.
(a) A’ + A = 1
A | A’ | A’+A |
0 | 1 | 1 |
1 | 0 | 1 |
(b) A’ A = 0
A | A’ | A’ A |
0 | 1 | 0 |
1 | 0 | 0 |
T10.
(a) A + A’ B = A + B
A | B | A’ | A’ B | A+A’B | A+B |
0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 1 |
(b) A ( A’ + B) = A B
A | B | ‘A’ | A’+B | A(A’+B) | AB |
0 | 0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 1 |
T11.Theorema De Morgan's
(a) ( A + B)’ = A’ B’
A | B | A’ | B’ | (A+B)’ | A’B’ |
0 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 |
(b) ( A B )’ = A’ + B’
A | B | A’ | B’ | (A B)’ | A’+B’ |
0 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 |
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