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## Main Question or Discussion Point

Hi everyone,

I've got a test tomorrow and while working through a practice test I got stuck. Here is the problem:

In the question below suppose P(x,y) is a predicate and the universe for the variables x and y is {1,2,3}. Suppose P(1,3), P(2,1), P(2,2), P(2,3), P(2,3), P(3,1), P(3,2) are true, and P(x,y) is false otherwise. Determine whether the following statements are true.

∀y∃x(P(x,y) → P(y,x)).

I understand that to find the truth value of a statement I should loop through each combination of values and if any result in False the statement is False. However, I'm not sure how I would loop through this one as x and y don't seem to be doing anything.

Any help would be appreciated.

I've got a test tomorrow and while working through a practice test I got stuck. Here is the problem:

In the question below suppose P(x,y) is a predicate and the universe for the variables x and y is {1,2,3}. Suppose P(1,3), P(2,1), P(2,2), P(2,3), P(2,3), P(3,1), P(3,2) are true, and P(x,y) is false otherwise. Determine whether the following statements are true.

∀y∃x(P(x,y) → P(y,x)).

I understand that to find the truth value of a statement I should loop through each combination of values and if any result in False the statement is False. However, I'm not sure how I would loop through this one as x and y don't seem to be doing anything.

Any help would be appreciated.