The document discusses several laws and properties related to Boolean algebra including: 1) Associative laws which state that operations combine in predictable ways regardless of grouping. 2) Commutative laws which state that the order of operands does not change the result. 3) Idempotent laws which state that an operand combined with itself is itself. 4) Identity laws which define operands that do not change the value of other operands. 5) Absorption laws which define relationships between operands combined in different ways. 6) Dominance laws which define the effect of combining an operand with 1 or 0. 7) Involution laws which define the effect of applying a logical complement twice. 8) Complement laws

4. a b a.b
0 0 0
0 1 0
1 0 0
1 1 1
a b a + b
0 0 0
0 1 1
1 0 1
1 1 1

5. a ā
0 1
1 0

7. 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

10. a. Hukum Asosiatif
(i) a + (b + c) = (a + b) + c
(ii) a . (b . c) = (a . b) . c
b. Hukum Komutatif
(i) a + b = b + a
(ii) a . b = b . A
c. Hukum Idempoten (Hukum Perluasan)
(i) a + a = a
(ii) a . a = a
d. Hukum Identitas
(i) a + 0 = a
(ii) a . 1 = a
e. Hukum Absorbsi
(i) a + ( a . b ) = a
(ii) a ( a + b ) = a
(iii) a + ( a’ . b ) = a + b
(iv) a ( a’ + b ) = a.b
f. Hukum dominansi
(i) a.1 = a
(ii) a+0 = a
(iii) a+1 = 1
(iv) a . 0 = 0
g. Hukum involusi
(i) (a’)’ = a
h. Hukum Komplementasi
(i) a + a’ = 1
(ii) a . a’ = 0
i. Hukum distributif:
(i) a + ( b . c ) = ( a + b ) ( a + c )
(ii) a ( b + c) = a . b + a . c
j. Hukum De Morgan
(i) (a + b)’ = a’. b’
(ii) (a . b)’ = a’ + b’

15. x y z f(x,y,z) = xyz’ + x
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1

17. x y z f=x’y’z + x’yz + xy’g g =x’z + xy
0 0 0 0 0
0 0 1 1 1
0 1 0 0 0
0 1 1 1 1
1 0 0 1 1
1 0 1 1 1
1 1 0 0 0
1 1 1 0 0

20. x y
Minterm Maxterm
Suku Lambang Suku Lambang
0 0 x’y’ m0 x + y M0
0 1 x’y m1 x + y’ M1
1 0 xy’ m2 x’ + y M2
1 1 xy m3 x’ + y’ M3

21. x y z
Minterm Maxterm
Suku Lambang Suku Lambang
0 0 0 x’y’z’ m0 x + y + z M0
0 0 1 x’y’z m1 x + y + z’ M1
0 1 0 x’yz’ m2 x + y’ + z M2
0 1 1 x’yz m3 x + y’ + z’ M3
1 0 0 xy’z’ m4 x’ + y + z M4
1 0 1 xy’z m5 x’ + y + z’ M5
1 1 0 xyz’ m6 x’ + y’ + z M6
1 1 1 xyz m7 x’ + y’ + z’ M7

22. x y z x’y’z xy’z’ xyz f(x,y,z)
0 0 0 0 0 0 0
0 0 1 1 0 0 1
0 1 0 0 0 0 0
0 1 1 0 0 0 0
1 0 0 0 1 0 1
1 0 1 0 0 0 0
1 1 0 0 0 0 0
1 1 1 0 0 1 1

27. x’y’ x’y
xy’ xy

28. x’y’z
’
x’y’z x’yz x’yz’
xy’z’ xy’z xyz xyz’

30. w’x’y’z’ w’x’y’z w’x’yz w’x’yz’
w’xy’z’ w’xy’z w’xyz w’xyz’
wxy’z’ wxy’z wxyz wxyz’
wx’y’z’ wx’y’z wx’yz wx’yz’