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I have this statement (it's translated from a different language): "if x divides y and y divides x, then x = y"

I want to write that statement predicate-logical symbols. I'm new to this so my question is if my attempt is correct. If not please answer what is wrong and how to fix it thanks.

My attempt:

$(x | y) \land (y | x) \rightarrow x = y$

To my knowledge there isn't a "divides" symbol specific to predicate-logic so I just used | for it. Parenthesis around x|y is to know what divides what. $\land$ means and. The arrow pointing to the right means that if the left is true then it means that the statement on the right of the arrow true as well. Is this correct?

Bioelli
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1 Answers1

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Maybe this counts as an answer and not just a comment.

Your work seems fine. The only issue is if you are learning a specific syntax.

As you said the "$\mid$" symbol is often used for divides. I would approve of its use here, but maybe the syntax in your situation wouldn't allow for it.

Your use of parentheses seems fine to me, but sometimes parentheses are used to mean something else. For example, instead of $\forall x$, I've seen $(x)$. Does your syntax allow your use of parentheses? Again, I would think it is ok.

Lastly, if you wanted to get really specific, you have to choose an order of reading connectives. The format of your answer is $A\wedge B \to C$. Technically, that could mean either $(A \wedge B) \to C$ or $A \wedge (B \to C)$. The usual interpretation is the first, making your work correct.

I think you are ok. I just saw an opportunity to be pedantic and disguise it as being helpful :)

J126
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