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August 22, 2017 01:16
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elementary propositional logic in APL
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| ⍝ ex. 1 | |
| ~((1 ∧ 0) ∨ (0 ↔ 1)) → ~(1 ∨ 0) | |
| ⍝ ~(0 ∨ 0) → ~(1 ∨ 0) | |
| ⍝ 1 → ~1 | |
| ⍝ 1 → 0 | |
| ⍝ 0 | |
| ⍝ ex. 2 | |
| ⍝ considering: | |
| ⍝ v(p) = 0 | |
| ⍝ v(q) = 1 | |
| ⍝ v(r) = 1 | |
| ⍝ ex. 3 | |
| (p → ~q) ∨ ~(r ∧ q) | |
| ⍝ (0 → ~1) ∨ ~(1 ∧ 1) | |
| ⍝ (0 → 0) ∨ ~1 | |
| ⍝ 1 ∨ 0 | |
| ⍝ 1 | |
| ⍝ ex. 4 | |
| (~ (p ↔ q) ∧ r) ∧ (p ∧ q ∧ ~ r) | |
| ⍝ (~ (0 ↔ 1) ∧ 1) ∧ (0 ∧ 1 ∧ ~ 1) | |
| ⍝ (~ 0 ∧ 1) ∧ (1 ∧ ~ 0) | |
| ⍝ ~ 1 ∧ (1 ∧ 1) | |
| ⍝ 0 ∧ 1 | |
| ⍝ 0 | |
| ⍝ ex. 5 | |
| ((p ↔ q) ^ r) ∨ (p ^ q ^ ~ r) | |
| ⍝ ((0 ↔ 1) ^ 1) ∨ (0 ^ 1 ^ ~ 1) | |
| ⍝ (0 ^ 1) ∨ (0 ^ ~ 1) | |
| ⍝ 0 ∨ (0 ^ 0) | |
| ⍝ 0 ∨ 0 | |
| ⍝ 0 |
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