Welcome To My World

Soal
A. Ubahlah pernyataan berikut dalam bentuk representasi logika proposisi dan predikat
1. Karjo adalah seorang laki-laki
2. Karjo adalah orang Jawa
3. Karjo lahir pada tahun 1840
4. Setiap laki-laki pasti akan mati
5. Semua orang Jawa mati pada saat Krakatau meletus tahun 1883
6. Setiap orang pasti mati setelah hidup lebih dari 150 tahun
7. Sekarang tahun 2010
8. Mati berarti tidak hidup
9. Jika seseorang mati, maka beberapa waktu kemudian dia pasti dianggap mati
B. Apakah Karjo masih hidup sekarang dengan metode Backward ?

Jawaban:
A.
1. Laki-laki(Karjo)
2. Jawa(Karjo)
3. Lahir(Karjo,1840)
4. ∀x : laki-laki(x) → pastimati(x)
5. Meletus(Krakatau, 1883) ∧ ∀x : [Jawa(x) → mati(x, 1883)
6. ∀x : ∀thn1 : ∀thn2 : pastimati(x) ∧ lahir(x, thn1) ∧ lahir(x, thn2) ∧ lebihdari(thn2 – thn1, 150) → mati(x, thn2)
7. Sekarang ≡ 2010
8. ∀x : ∀y : [mati(x,y) → ¬hidup(x,y) ] ∧ [¬hidup(x,y) → mati(x,y)]
9. ∀x : ∀thn1 : ∀thn2 : mati(x, thn1) ∧ lebihdari(thn2 – thn1) → mati(x, thn2)

B.
Dari pernyataan diatas akan dibuktikan Karjo tidak hidup sekarang dengan penalaran backward : ¬hidup (karjo, sekarang)

¬hidup (karjo, sekarang)
↑ (8, subtitusi)
Mati(karjo, sekarang)
↑ (9, subtitusi)
Mati(karjo, thn1) ∧ lebihdari(sekarang, thn1)
↑ (5, subtitusi)
Jawa(Karjo) ∧ lebihdari(sekarang, 1883)
↑ (2)
Lebihdari(sekarang, 1883)
↑ (7, subtitusi)
Lebihdari(2010, 1883)
↑ (menghitung lebihdari)
Nil

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