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Using Truth Tables to Summarize Interpretations (Optional)

16 六月, 2015 - 14:44
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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