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| author | Manuel Palenzuela <manuelpalenzuelamerino@gmail.com> | 2019-10-10 00:09:28 +0100 |
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| committer | Manuel Palenzuela <manuelpalenzuelamerino@gmail.com> | 2019-10-10 00:09:28 +0100 |
| commit | 8866b7a72d97dd0c4f415acc8293c240a27f1801 (patch) | |
| tree | 2ce4e427606e303928aee3a5fb0efbc258468e1d /Maths | |
| download | Homework-8866b7a72d97dd0c4f415acc8293c240a27f1801.tar.gz Homework-8866b7a72d97dd0c4f415acc8293c240a27f1801.tar.bz2 Homework-8866b7a72d97dd0c4f415acc8293c240a27f1801.zip | |
Bruh Init
Diffstat (limited to 'Maths')
| -rw-r--r-- | Maths/Prepositional_Formulas | 143 |
1 files changed, 143 insertions, 0 deletions
diff --git a/Maths/Prepositional_Formulas b/Maths/Prepositional_Formulas new file mode 100644 index 0000000..b0b25fd --- /dev/null +++ b/Maths/Prepositional_Formulas @@ -0,0 +1,143 @@ +* 1 +a. + S = Sunny + I = Ice cream + B = Beer + + S => (I V B) + +b. + F = Earth flat + G = Earth a globe + H = Global warming is hoax + + F => !G => H + +c. + L = Attended lectures + H = Homework done + S = Studied for exam + P = Passed maths + + (L A H A S ) <=> P + +d. + S = You smell essential oils + C = You will be cured + + N = Modern medicine doesnt work + + (S => C) <=> N + +* 2 + +a. (P V !Q) <=> (Q => P) + + P Q P V !Q Q => P + 1 1 1 1 + 1 0 1 1 + 0 1 0 0 + 0 0 1 1 + +b. (P => (Q => R)) <=> ((P A Q) => R) + + R Q P P => (Q => R) (P A Q) => R + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 1 1 + 0 0 0 1 1 + 0 0 1 1 1 + 0 1 0 1 1 + 1 0 1 1 1 + 0 1 1 0 0 + +c. ((P => Q) V (P => R)) <=> (P => (Q V R)) + + R Q P (P => Q) V (P => R) P => (Q V R) + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 1 1 + 0 0 0 1 1 + 0 0 1 0 0 + 0 1 0 1 1 + 1 0 1 1 1 + 0 1 1 1 1 + +d. (!(P A !Q) V (R => 0)) <=> ((P A R) => Q) + + R Q P !(P A !Q) V (R => 0) (P A R) => Q + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 1 1 + 0 0 0 1 1 + 0 0 1 1 1 + 0 1 0 1 1 + 1 0 1 0 0 + 0 1 1 1 1 + +* 3 + +a. (P A (Q V R)) and ((P A Q) V P) = 2nd follows from 1st + + R Q P P A (Q V R) (P A Q) V P + 1 1 1 1 1 + 1 1 0 0 0 + 1 0 0 0 0 + 0 0 0 0 0 + 0 0 1 0 1 + 0 1 0 0 0 + 1 0 1 0 1 + 0 1 1 1 1 + +b. (P V (Q A R)) and ((P V Q) A (P V R)) = 1st follows from 2nd + + R Q P P V (Q A R) (P V Q) A (P V R) + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 0 0 + 0 0 0 0 0 + 0 0 1 1 0 + 0 1 0 0 0 + 1 0 1 1 1 + 0 1 1 1 1 + +c. (P => (Q => R)) and ((P => Q) => R) = 1st follows from 2nd + + R Q P P => (Q => R) (P => Q) => R + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 1 1 + 0 0 0 1 0 + 0 0 1 1 1 + 0 1 0 1 0 + 1 0 1 1 1 + 0 1 1 0 0 + +d. (0 => (P A Q)) and (P V Q) = 1st follows from 2nd + + R Q P 0 => (P A Q) P V Q + 1 1 1 1 1 + 1 1 0 1 1 + 1 0 0 1 0 + 0 0 0 1 0 + 0 0 1 1 1 + 0 1 0 1 1 + 1 0 1 1 1 + 0 1 1 1 1 + + +* 5 + +B = Bob says truth +A = Alice says truth +C = Carol says truth + + B A C !B => !C A A C !A A !B + 1 1 1 1 1 0 + 1 1 0 1 0 0 + 1 0 0 1 0 0 + 0 0 0 1 0 1 + 0 0 1 0 0 1 + 0 1 0 1 0 0 + 1 0 1 0 0 0 + 0 1 1 0 1 0 |