Tugas 4.A

1. Hukum Komutatif

a. A+B=B+A

A	B	A+B	B+A	A+B=B+A
0 0 1 1	0 1 0 1	0 1 1 1	0 1 1 1	√ √ √ √

b. AB=BA

A	B	AB	BA	AB=BA
0 0 1 1	0 1 0 1	0 0 0 1	0 0 0 1	√ √ √ √

2. Hukum Asosiatif

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

A	B	C	A+B	B+C	(A+B)+C	A+(B+C)	(A+B)+C = A+(B+C)
0 0 0 0 1 1 1 1	0 0 1 1 0 0 1 1	0 1 0 1 0 1 0 1	0 0 1 1 1 1 1 1	0 1 1 1 0 1 1 1	0 1 1 1 1 1 1 1	0 1 1 1 1 1 1 1	√ √ √ √ √ √ √ √

b. (AB)C = A(BC)

A	B	C	AB	BC	(AB)C	A(BC)	(AB)C = A(BC)
0 0 0 0 1 1 1 1	0 0 1 1 0 0 1 1	0 1 0 1 0 1 0 1	0 0 0 0 0 0 0 1	0 0 0 1 0 0 0 1	0 0 0 0 0 0 0 1	0 0 0 0 0 0 0 1	√ √ √ √ √ √ √ √

3. Hukum Distributif

a. A(A+C) = AB+AC

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

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

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

4. Hukum Identity

a. A+A = A

A	A+A	A+A=A
0 0 1 1	0 0 1 1	√ √ √ √

b. AA = A

A	AA	AA=A
0 0 1 1	0 0 1 1	√ √ √ √

5. a. AB+AB = A

A	B	B(invers)	AB	AB(inverse)	A
0 0 1 1	0 1 0 1	1 0 1 0	0 0 0 1	0 0 1 0	0 0 1 1

b. (A+B)(A+B) = A

A	B	B(invers)	A+B	A+B(inverse)	A
0 0 1 1	0 1 0 1	1 0 1 0	0 1 1 1	1 0 1 1	0 0 1 1

6. Hukum Redudansi

a. A+AB = A

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

b. A+AB = A

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

7. a. 0+A = A

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

b. 0A = 0

A	0A	0
0 0 1 1	0 0 0 0	0 0 0 0

8. a. 1+A = 1

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

b. 1A = A

A	1A
0 0 1 1	0 0 1 1

9. Theorema De Morgan

a.

A	B	A(invers)	B(inverse)	A+B	(A+B)inverse	A(inverse)B(inverse)
0	0	1	1	0	1	1
0	1	1	0	1	0	0
1	0	0	1	1	0	0
1	1	0	0	1	0	0

b.

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