Translate the following sentence into first-order logic. John is the tallest stu

Question

Translate the following sentence into first-order logic. John is the tallest student in his class. Assume class(x) means that x is in John's class and taller(x, y) means that x is taller than y and that John refers to John. Suppose P(x, y) means that x > y where x and y are integers. Which of the following formulas are true in this interpretation? forall x exist y P(x, y) forall y exist x P(x, y) forall x, z exist y(P(x, y) logicaland P(y, z)) Let I be the interpretation that interprets P(x, y) as x + y = 1 and assume that the domain of I is the set {0, 1} of integers. Does I satisfy the formula forall x exist y P(x, y)?

Explanation / Answer

1)

Let us denote

John : John

Class(x) : x is John's class

Taller( x , y ) : x is taller than y

The the statement " John is the tallest student in his class " can be written in symbolic form as follows:

( y) ( Class(y) Taller(John , y ) )

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