Consider the formula ϕ = R (x, y) ⇒ S (x, y) ∧¬T (x, y). As yet, we haven't said anything about the interpretations of these three relations. But, we do know that each of R (x, y), S (x, y), and T (x, y) can either be true or false. Thus, treating each of those as a proposition, we can describe the formula's truth under different interpretations.
|
R (x, y) |
S (x, y) |
R (x, y) |
[U+03D5] |
|
false |
false |
false |
true |
|
false |
false |
true |
true |
|
false |
true |
false |
true |
|
false |
true |
true |
true |
|
true |
false |
false |
false |
|
true |
false |
true |
false |
|
true |
true |
false |
true |
|
true |
true |
true |
false |
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