Formulas in predicate logic/2 places
Formulas in predicate logic 
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Two different variables
[edit | edit source]2 * 
A232598(2,2) = 6
| Sentence | Formula | Example 5x5 | All 2×2 | All 3×3 |
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| Someone loves someone. Someone is loved by someone. |
∃x∃y Pxy ∃y∃x Pxy  e12 |
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| Everyone is loved by someone. | ∀y∃x Pxy a2 e1 |
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| Everyone loves someone. | ∀x∃y Pxy a1 e2 |
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| Someone loves everyone. | ∃x∀y Pxy e1 a2 |
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| Someone is loved by everyone. | ∃y∀x Pxy e2 a1 |
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| Everyone loves everyone. Everyone is loved by everyone. |
∀x∀y Pxy ∀y∀x Pxy  a12 |
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Both variables coinciding
[edit | edit source]2 * A232598(2,1) = 2
| Sentence | Formula | Example 5x5 | All 2×2 | All 3×3 |
|---|---|---|---|---|
| Someone loves himself. | ∃x Pxx.svg){kind=small} e(12) |
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| Everyone loves himself. | ∀x Pxx.svg){kind=small} a(12) |
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