Logika Informatika
LATIHAN SOAL
1. p = Febi pintar
q = Febi hidup bahagia
Ubah pernyataan berikut menjadi bentuk logika !
a) Febi tidak pintar
b) Febi pintar dan hidup bahagia
c) Febi hidup bahagia jika dan hanya jika ia pintar
Penyelesaian :
a) ~ p
b) p ˄ q
c) q ↔ p
2. Misalkan A, B dan C adalah variabel proposional :
A = anda sakit flu
B = anda ujian
C = anda lulus
Ubah ekspresi berikut menjadi pernyataan dalam bahasa Indonesia !
1) ~ A → B
2) B → ~ C
3) (A ˄ B) → C
4) (A → ~ C) ˅ (B → ~ C)
Penyelesaian :
1) Jika anda tidak sakit flu maka anda ujian
2) Jika anda ujian maka anda tidak lulus
3) Anda sakit flu dan anda ujian maka anda lulus
4) Jika anda sakit flu maka anda tidak lulus atau jika anda ujian maka anda tidak lulus
3. Buatlah table kebenaran dengan semua kemungkinan nilai kebenaran dari ekspresi-ekspresi logika berikut ini :
a) ~ (~A ˄ ~B)
b) A ˄ (A ˅ B)
c) ((~A ˄ (~B ˄ C)) ˅ (B ˄ C)) ˅ (A ˄ C)
d) (A ˄ B) ˅ (((~A ˄ B) → A) ˄ ~B)
e) (A → B) ↔ (~B → ~A)
f) A ˄ ((C ˅ B) ↔ ~C)
g) ~((A ˄ B) → ~C) ˅ A
Penyelesaian :
a)
|
A |
B |
~A |
~B |
~A˄~B |
~(~A^~B) |
|
T |
T |
F |
F |
F |
T |
|
T |
F |
F |
T |
F |
T |
|
F |
T |
T |
F |
F |
T |
|
F |
F |
T |
T |
T |
F |
b)
|
A |
B |
A˅B |
A˄(A˅B) |
|
T |
T |
T |
T |
|
T |
F |
T |
T |
|
F |
T |
T |
F |
|
F |
F |
F |
F |
c)
|
A |
B |
C |
̴A |
̴B |
̴C |
( ̴B˄C) |
(B˄C) |
(A˄C) |
( ̴B˄C)˅ ̂(B^C) |
( ̴A^( ̴B^C)ˇ(B^C) |
(( ̴A^( ̴B^C)˅(B^C))˅(A^C) |
|
T |
T |
T |
F |
F |
F |
F |
T |
T |
T |
F |
T |
|
T |
T |
F |
F |
F |
T |
F |
F |
F |
F |
F |
F |
|
T |
F |
T |
F |
T |
F |
T |
F |
T |
T |
F |
T |
|
T |
F |
F |
F |
T |
T |
F |
F |
F |
F |
F |
F |
|
F |
T |
T |
T |
F |
F |
F |
T |
F |
T |
T |
T |
|
F |
T |
F |
T |
F |
T |
F |
F |
F |
F |
F |
F |
|
F |
F |
T |
T |
T |
F |
T |
F |
F |
T |
T |
T |
|
F |
F |
F |
T |
T |
T |
F |
F |
F |
F |
F |
F |
d)
|
A |
B |
̴A |
̴B |
(A^B) |
( ̴A^B) |
( ̴A^B)→A |
( ̴A^B)→A)^ ̴B |
(A^B)˅((( ̴A^B)→A)^ ̴B |
|
T |
T |
F |
F |
T |
F |
T |
F |
T |
|
T |
F |
F |
T |
F |
F |
T |
T |
T |
|
F |
T |
T |
F |
F |
T |
F |
F |
F |
|
F |
F |
T |
T |
F |
F |
T |
T |
T |
e)
|
A |
B |
C |
̴A |
̴B |
̴C |
CˇB |
(CˇB)↔ ̴C |
A^((CˇB)↔ ̴C |
||
|
T |
T |
T |
F |
F |
F |
T |
F |
F |
||
|
T |
T |
F |
F |
F |
T |
T |
T |
T |
||
|
T |
F |
T |
F |
T |
F |
T |
F |
F |
||
|
T |
F |
F |
F |
T |
T |
F |
F |
F |
||
|
F |
T |
T |
T |
F |
F |
T |
F |
F |
||
|
F |
T |
F |
T |
F |
T |
T |
T |
F |
||
|
F |
F |
T |
T |
T |
F |
T |
F |
F |
||
|
F |
F |
F |
T |
T |
T |
F |
F |
F |
||
f)
|
A |
B |
C |
̴A |
̴B |
̴C |
(A^B) |
(A^B)→ ̴C |
̴((A^B)→ ̴C) |
̴((A^B)→ ̴C)˅A |
|
T |
T |
T |
F |
F |
F |
T |
F |
T |
T |
|
T |
T |
F |
F |
F |
T |
T |
T |
F |
T |
|
T |
F |
T |
F |
T |
F |
F |
T |
F |
T |
|
T |
F |
F |
F |
T |
T |
F |
T |
F |
T |
|
F |
T |
T |
T |
F |
F |
F |
T |
F |
F |
|
F |
T |
F |
T |
F |
T |
F |
T |
F |
F |
|
F |
F |
T |
T |
T |
F |
F |
T |
F |
F |
|
F |
F |
F |
T |
T |
T |
F |
T |
F |
F |
g)
|
A |
B |
̴A |
̴B |
A→B |
̴ B→ ̴A |
(A→B) ↔( ̴B→ ̴A) |
|
T |
T |
F |
F |
T |
T |
T |
|
T |
F |
F |
T |
F |
T |
F |
|
F |
T |
T |
F |
T |
F |
F |
|
F |
F |
T |
T |
T |
T |
T |
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