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I have the statement "been(x,y)" which means " x has been to y" x is a set of names and y is a set of place. I'm trying to figure out how to write "Every person has been to at least two different places." using only quantifiers and been(x,y) but I'm lost. Would I need to create a new statement like P(x) or a new variable and how do I include the at least function? I'd really appreciate the help

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    Try first with "Every person has been to at least one place." $\forall x \exists y \ \text {been}(x,y)$. – 2017-01-18
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    Now you can add the second place... $\exists y \exists z \ldots$ taking care of the fact that they must be different ($\ne$). – 2017-01-18
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    "Every person" is symbolized with $\forall x$ while "at least one place" is $\exists y$. – 2017-01-18
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    Okay, I understand...so I'd introduce a new variable for the second place 'z' – 2017-01-19
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    `∀x,∃y,∃z,y≠z,been(x,y)` is this right? – 2017-01-19
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    does this mean that if `∃y` means "at least one place" then `∃y∃z` would mean "at least two places"with z representing a second element from the 'y' set? – 2017-01-19
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    @DrewU that says "Every $x$ has been to some place $y$ and there is something that is not $y$." – 2017-01-19
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    Correct : $∃y∃z ( y \ne z \land \ldots)$ specify there at least two **distinct** places such that ... – 2017-01-19

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