TUGAS 4A

Hukum Aljabar Boolean

1. Hukum Komutatif

(a) A + B = B + A

(b) A B = B A

Nilai Tabel Kebenarannya

A	B	A+B	B+A
0	0	0	0
0	1	1	1
1	0	1	1
1	1	1	1

Nilai Hukum Komutatif Benar

2. Hukum Asosiatif

(a) (A + B) + C = A + (B + C)

(b) (b) (A B) C = A (B C)

Nilai Tabel Kebenarannya

A	B	C	A+B	B+C	AB	BC	(A+B)+C	A+(B+C)	(AB)C	A(BC)
0	0	0	0	0	0	0	0	0	0	0
0	0	1	0	1	0	0	1	1	0	0
0	1	0	1	1	0	0	1	1	0	0
0	1	1	1	1	0	1	1	1	0	0
1	0	0	1	0	0	0	1	1	0	0
1	0	1	1	1	0	0	1	1	0	0
1	1	0	1	1	1	0	1	1	0	0
1	1	1	1	1	1	1	1	1	1	1

Nilai Hukum Benar

3. Hukum Distributif

(a) A (B + C) = A B + A C

(b) A + (B C) = (A + B) (A + C)

Nilai Tabel Kebenaran

A	B	C	A+B	A+C	B+C	AB	AC	BC	A(B+C)	(AB)+(AC)	A+(BC)	(A+B)(A+C)
0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	1	0	1	1	0	0	0	0	0	0	0
0	1	0	1	0	1	0	0	0	0	0	0	0
0	1	1	1	1	1	0	0	1	0	0	1	1
1	0	0	1	1	0	0	0	0	0	0	1	1
1	0	1	1	1	1	0	1	0	1	1	1	1
1	1	0	1	1	1	1	0	0	1	1	1	1
1	1	1	1	1	1	1	1	1	1	1	1	1

Nilai Hukum Benar

4. Hukum Identity

(a) A + A = A

(b) A A = A

Nilai Tabel Kebenaran

A	A+A	AA
0	0	0
1	1	1

Nilai Hukum Benar

5.

(a) AB+AB’=A
(b) (A+B)(A+B’)=A

Nilai Tabel Kebenaran

A	B	B’	AB	AB’	A+B	A+B’	AB+AB’	(A+B)(A+B’)
0	0	1	0	0	0	1	0	0
0	1	0	0	0	1	0	0	0
1	0	1	0	1	1	1	1	1
1	1	0	1	0	1	1	1	1

Nilai Hukum Benar

6. Hukum Redudansi

(a) A + A B = A

(b) A (A + B) = A

Nilai Tabel Kebenaran

A	B	AB	A+B	A+AB	A(A+B)
0	0	0	0	0	0
0	1	0	1	0	0
1	0	0	1	1	1
1	1	1	1	1	1

Nilai Hukum Benar

7.

(a) 0 + A = A

(b) 0 A = 0

Nilai Tabel Kebenaran

A	0	0+A	0A
0	0	0	0
1	0	1	0

Nilai Hukum Benar

8.

(a) 1 + A = 1
(b) 1 A = A

Nilai Tabel Kebenaran

A	1	1+A	1A
0	1	1	0
1	1	1	1

Nilai Hukum Benar

9.

(a) A’ + A = 1
(b) A’A = 0

Nilai Tabel Kebenarannya

A	A’	A+A’	AA’
0	1	1	0
1	0	1	0

Nilai Hukum Benar

10.

(a) A + A’B = A+B

(b) A (A’+B) = AB

Nilai Tabel Kebenaran

A	B	A’	AB	(AB)’	A+B	A’+B	A+A’B	A(A’+B)
0	0	1	0	0	0	1	0	0
0	1	1	0	1	1	1	1	0
1	0	0	0	0	1	0	1	0
1	1	0	1	0	1	1	1	1

Nilai Hukum Benar

11. TheoremaDe Morgan's

(a) (A+B)’ = A’B’
(b) ( AB )’= A’ + B ‘

Nilai Tabel Kebenaran

A	B	A+B	AB	(A+B)’	(AB)’	A’	B’	A’B’	A’+B’
0	0	0	0	1	1	1	1	1	1
0	1	1	0	0	1	1	0	0	1
1	0	1	0	0	1	0	1	0	1
1	1	1	1	0	0	0	0	0	0

Nilai Hukum Benar