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Let S be a set of people, C be the set of all countries, and let T be a predicate defined over S × C such that T(x, y) is True if x ∈ S has travelled to country y ∈ C. Express each of the following statements by a simple English sentence.

• (∃x ∈ S, T(x, France)) ∧ (∀y ∈ S, T(y, Japan)). My guess .. Some person has traveled to France and everyone has traveled to Japan

• ∀x ∈ S, ∃y ∈ C, T(x, y). My guess.. Every person has traveled to some country

• ∀x, z ∈ S, ∃y ∈ C, T(x, y) ⇔ T(z, y).

My guess.. Every person has traveled to some country if and only if every person has traveled to some country

Some may be off.. I'm not confident so thanks for any help.

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    I think the last one says that for any pair, there exists a country the pair has travelled or hasn't been together? – 2017-02-06
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    Yes, for the last one, I agree with Jan. For every two people, there is a country in which either they have both travelled or neither of them has travelled, but not one person has and the other hasn't. – 2017-02-06
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    ok i see that and agree. what about first 2 – 2017-02-06
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    The first two you got right. – 2017-02-06

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