Give clear English translations of the following sentences of FOL. Which of the

Question

Give clear English translations of the following sentences of FOL. Which of the following are logically equivalent and which are not? Explain your answers. THERE EXISTS!xTove(x) [Remember that the notation THERE EXISTS is an abbreviation, as explained above.] THERE EXISTSx FOR ALLy [Tove(y) rightarrow y = x] THERE EXISTSxFOR ALLy (Tove(y) leftrightarrow y = x] FOR ALLx FOR ALLy [(Tove(x) logical and Tove(y)) rightarrow x = y] FOR ALLx FOR ALLy [(Tove(x) logical and Tove(y)) liftrightarrow x = y]

Explanation / Answer

1. there does not exists x for dove x

2.there exists x for all y such that if tovey exists then y =x

3.there exists x for all y if an only if y = x

4.there exists x for all y such that if tove x and tove y exists then x =y

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