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I was trying to translate the following sentence into predicate logic: “Some student in this class has taken a course in Java.”

Assuming the domain/universe is all people, then the correct translation is $\exists x(S(x) \land J(x))$, but $\exists x(S(x) \to J(x))$ is not correct. Can someone explain why this is?

Nico
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charls defoes
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Nov 08 '22 at 17:48
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    I suppose you are trying to use the $\exists$ symbol but all I see on my browser is a little box with some numbers inside it. Please use MathJax to write your formulas so that they will show up correctly: http://math.stackexchange.com/help/notation Also check the formatting of your question as it appears in a browser: you have two formulas combined with each other that I don't think you wanted to combine. You may need to insert a blank line in your edit window in order to get the effect you want. – David K Nov 08 '22 at 17:52
  • Do you really want to know how to translate $\exists x,(S(x)\implies J(x))$ into plain language? See https://math.stackexchange.com/questions/431842/implication-with-a-there-exists-quantifier – David K Nov 08 '22 at 18:00

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I'm assuming the square shape is supposed to be the existential quantifier. For the future, I highly recommend using LaTeX because it lets you easily type the $\exists$, $\land$, and $\to$ symbols.

Anyway, here's the answer:

$\exists x(S(x) \land J(x))$ is correct because it is saying "there exists someone who is a student, and is taking Java", which is equivalent to the original sentence of "Some student in this class has taken a course in Java."

$\exists x(S(x) \to J(x))$ is not correct, because it is saying "there exists someone, such that if they are a student, then they are taking Java". It doesn't actually state that there is a student who satisfies both properties.

If it clarifies things, it's just like the difference between "Someone just had a heart attack and had to go to the hospital!!" and "There is someone such that if that person has a heart attack, then they will have to go to the hospital". The first one will result in an "oh no!" response, the second will result in a rather confused "...duh."

Nico
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