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  1. Everything is greater than or equa to itself;
  2. For evert number n, the resut of adding n to 9 is greater than or equal to 9;
  3. Everything has something greater than it.

This is for my semantics homework, I tried to first question, but I think I got it wrong, My answer is ∀X1[greater(X1)∨equal(X2)]. Please correct my first question and help me with next two questions. Thank you so much!

Karen
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2 Answers2

1
  1. $\forall x[x\mbox{ is greather than }x \vee x\mbox{ is equal to x }]$

2.$\forall n:[ n+9\mbox{ is greather than }9 \vee n+9 \mbox{ is equal to }9]$ Where $n+9$ denotes the result of adding n to 9

  1. $\forall x, \exists y:[ y\mbox{ is greather than }x]$
L F
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  • Assume that in $U$ you have the order-relation given by $(U,<)$ – L F Mar 29 '15 at 03:37
  • Thanks so much. I have a question for all the examples that I've seen in the handouts involve brackets. Ex. Everything is black or white: ∀x2[black(X2)∨white(X2)]. Do you think these two questions should include brackets too? – Karen Mar 29 '15 at 03:39
  • emm, you can do this: let $p(x):{x\in U: \mbox{ x is black }}$ and $q(x):{x\in U: \mbox{ x is white }}$ two propositions, then $\forall x\in U, p(x)\vee q(x)$ Also brackets notation is ok. – L F Mar 29 '15 at 03:42
  • If it is helpfull for you, you can vote-up in the check place closer the answer. – L F Mar 29 '15 at 03:44
  • Sorry for having so more questions, but in our class we don't use "U" in translation. "everything is black or white ->∀x2[black(X2)∨white(X2)]" that's the example that my teacher gave us. She wants us to have same format as that example. So in the three examples I post it, is there anyway I can avoid using U and add bracket to it to make it simiar to the example? I really appreciate your help!! – Karen Mar 29 '15 at 03:50
  • Okey, i fixed it. You can check now and if you have some question let me know. Don't forget vote-up if everything is okay. – L F Mar 29 '15 at 03:59
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The first can be written as $\forall{x}.x \ge x$, or $\forall{x}.x \gt x \vee x = x$ if the language doesn't include $\ge$. Your answer looks almost right, but the predicates "greater" and "equal" each require two arguments and you have an unquantified variable X2. In the same style I would write the answer as ∀X1[greater(X1,X1)∨equal(X1,X1)].

Can you take it from here?

Dan Brumleve
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