Formulas in predicate logic/2 places

Formulas in predicate logic Rdrup.svg

Two different variablesEdit

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 coincidingEdit

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)