Tentukan hasil dari tabel diatas p q r ~pvq p^~r q - > r ~p

Tabel kebenaran lengkap telah dihitung untuk setiap proposisi.

Pembahasan

Untuk menentukan hasil dari tabel tersebut, kita perlu menganalisis setiap kolom berdasarkan logika proposisi:

Diketahui:
B = Benar (True)
S = Salah (False)

Kolom-kolom yang perlu dianalisis:
- p
- q
- r
- ~pvq
- p^~r
- q -> r
- ~p -> r
- q^r

Kita perlu mengisi tabel kebenaran berdasarkan nilai p, q, dan r yang diberikan di setiap baris.

Baris 1: p=B, q=B, r=B
- ~pvq: ~B v B = S v B = B
- p^~r: B ^ ~B = B ^ S = S
- q -> r: B -> B = B
- ~p -> r: ~B -> B = S -> B = B
- q^r: B ^ B = B

Baris 2: p=B, q=B, r=S
- ~pvq: ~B v B = S v B = B
- p^~r: B ^ ~S = B ^ B = B
- q -> r: B -> S = S
- ~p -> r: ~B -> S = S -> S = B
- q^r: B ^ S = S

Baris 3: p=B, q=S, r=B
- ~pvq: ~B v S = S v S = S
- p^~r: B ^ ~B = B ^ S = S
- q -> r: S -> B = B
- ~p -> r: ~B -> B = S -> B = B
- q^r: S ^ B = S

Baris 4: p=B, q=S, r=S
- ~pvq: ~B v S = S v S = S
- p^~r: B ^ ~S = B ^ B = B
- q -> r: S -> S = B
- ~p -> r: ~B -> S = S -> S = B
- q^r: S ^ S = S

Baris 5: p=S, q=B, r=B
- ~pvq: ~S v B = B v B = B
- p^~r: S ^ ~B = S ^ S = S
- q -> r: B -> B = B
- ~p -> r: ~S -> B = B -> B = B
- q^r: B ^ B = B

Baris 6: p=S, q=B, r=S
- ~pvq: ~S v B = B v B = B
- p^~r: S ^ ~S = S ^ B = S
- q -> r: B -> S = S
- ~p -> r: ~S -> S = B -> S = S
- q^r: B ^ S = S

Baris 7: p=S, q=S, r=B
- ~pvq: ~S v S = B v S = B
- p^~r: S ^ ~B = S ^ S = S
- q -> r: S -> B = B
- ~p -> r: ~S -> B = B -> B = B
- q^r: S ^ B = S

Baris 8: p=S, q=S, r=S
- ~pvq: ~S v S = B v S = B
- p^~r: S ^ ~S = S ^ B = S
- q -> r: S -> S = B
- ~p -> r: ~S -> S = B -> S = S
- q^r: S ^ S = S

Hasil tabel kebenaran yang lengkap adalah sebagai berikut:

p | q | r | ~pvq | p^~r | q -> r | ~p -> r | q^r
--|---|---|-------|-------|--------|--------|------
B | B | B | B     | S     | B      | B      | B
B | B | S | B     | B     | S      | B      | S
B | S | B | S     | S     | B      | B      | S
B | S | S | S     | B     | B      | B      | S
S | B | B | B     | S     | B      | B      | B
S | B | S | B     | S     | S      | S      | S
S | S | B | B     | S     | B      | B      | S
S | S | S | B     | S     | B      | S      | S