Consider the following two formulas interpreted over the domain {1,2}:

∃x: ∀y: p(x,y)

∀y: ∃x: p(x,y)

For which definition of p is the first formula "true" and the second formula "false"?

Question

Consider the following two formulas interpreted over the domain {1,2}:

∃x: ∀y: p(x,y) 
 
        ∀y: ∃x: p(x,y)

For which definition of  p  is the first formula "true" and the second formula "false"?

Answer

p(1,1)=true, p(1,2)=true, p(2,1)=true, p(2,2)=true

Answer

p(1,1)=true, p(1,2)=false, p(2,1)=true, p(2,2)=false

Answer

p(1,1)=false, p(1,2)=false, p(2,1)=false, p(2,2)=false

Answer

None

Answer

p(1,1)=true, p(1,2)=true, p(2,1)=false, p(2,2)=false

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