Formulas in predicate logic/2 places

Formulas in predicate logic

Two different variables

2 *  A232598(2,2) = 6

Sentence	Formula	Example 5x5	All 2×2	All 3×3
Someone loves someone. Someone is loved by someone.	∃x∃y Pxy ∃y∃x Pxy e12
Everyone is loved by someone.	∀y∃x Pxy a2 e1
Everyone loves someone.	∀x∃y Pxy a1 e2
Someone loves everyone.	∃x∀y Pxy e1 a2
Someone is loved by everyone.	∃y∀x Pxy e2 a1
Everyone loves everyone. Everyone is loved by everyone.	∀x∀y Pxy ∀y∀x Pxy a12

Both variables coinciding

2 *  A232598(2,1) = 2

Sentence	Formula	Example 5x5	All 2×2	All 3×3
Someone loves himself.	∃x Pxx e(12)
Everyone loves himself.	∀x Pxx a(12)