Buktikan bahwa ekspresi – ekspresi logika berikut ini
ekuivalen dengan menggunakan tabel kebenaran
1. ~A <-> B ≡ (~A
˅ B) ^ (~B ˅ A)
|
A
|
B
|
~A
|
~B
|
~A <-> B
|
~A ˅ B
|
~B ˅ A
|
(~A ˅ B) ^ (~B ˅ A)
|
|
T
|
T
|
F
|
F
|
F
|
T
|
T
|
T
|
|
T
|
F
|
F
|
T
|
T
|
F
|
T
|
F
|
|
F
|
T
|
T
|
F
|
T
|
T
|
F
|
F
|
|
F
|
F
|
T
|
T
|
F
|
T
|
T
|
T
|
Jadi . ~A <-> B ≡ (~A ˅ B) ^ (~B ˅ A) tidak bernilai
ekuivalen
2. A -> (~A ->
B) ≡ 1
|
A
|
B
|
~A
|
(~A -> B)
|
A -> (~A -> B)
|
|
T
|
T
|
F
|
F
|
T
|
|
T
|
F
|
F
|
F
|
T
|
|
F
|
T
|
T
|
T
|
F
|
|
F
|
F
|
T
|
T
|
F
|
Jadi A -> (~A -> B) ≡ 1 tidak bernilai ekuivalen
3. (A ˅ ~B) -> C ≡
(~A ^ B) ˅ C
|
A
|
B
|
C
|
~A
|
~B
|
(A ˅ B)
|
(A ˅ ~B) -> C
|
(~A ^ B)
|
(~A ^ B) ˅ C
|
|
T
|
T
|
T
|
F
|
F
|
T
|
T
|
F
|
T
|
|
T
|
T
|
F
|
F
|
F
|
T
|
F
|
F
|
F
|
|
T
|
F
|
T
|
F
|
T
|
T
|
T
|
F
|
T
|
|
T
|
F
|
F
|
F
|
T
|
T
|
F
|
F
|
F
|
Jadi (A ˅ ~B) -> C ≡
(~A ^ B) ˅ C bernilai ekuivalen
4. A -> (B -> C)
≡ (A -> B) -> C
|
A
|
B
|
C
|
(B -> C)
|
A -> (B -> C)
|
(A -> B)
|
(A -> B) -> C
|
|
T
|
T
|
T
|
T
|
T
|
T
|
T
|
|
T
|
T
|
F
|
F
|
F
|
T
|
F
|
|
T
|
F
|
T
|
T
|
T
|
F
|
T
|
|
T
|
F
|
F
|
T
|
T
|
F
|
T
|
Jadi A -> (B ->
C) ≡ (A -> B) -> C bernilai ekuivalen
5. A -> B ≡ ~(A ^
~B)
|
A
|
B
|
A -> B
|
~A
|
~B
|
~(A ^ ~B)
|
|
T
|
T
|
T
|
F
|
F
|
T
|
|
T
|
F
|
T
|
F
|
T
|
F
|
|
F
|
T
|
F
|
T
|
F
|
T
|
|
F
|
F
|
T
|
T
|
T
|
F
|
Jadi A -> B ≡ ~(A ^
~B) tidak bernilai ekuivalen
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