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I appologize all of you for late reply. I was not online. I have to know that how sentences are made like below such as first statement can also be made like "Bruno comes to the party while Angelo doesn't" I changed the order of the sentence is it ok? so are there rules to make this kind of sentences? like in first sentence, first clause is affermative 2nd is negative whereas 2nd sentence has made with Either or. or can I create more than 5 statements with different connectives?

Let’s consider a propositional language where

• A =“Angelo comes to the party”,

• B =“Bruno comes to the party”,

• C =“Carlo comes to the party”,

• D =“Davide comes to the party”.

How to make below sentences from above statements, are there rules? Formalize the following sentences:

  1. “Angelo comes to the party while Bruno doesn’t”

  2. “Either Carlo comes to the party, or Bruno and Davide don’t come”

  3. “If Angelo and Bruno come to the party, then Carlo comes provided that Davide doesn’t come”

  4. “Carlo comes to the party if Bruno and Angelo don’t come, or if Davide comes”

  5. “If Angelo comes to the party then Bruno or Carlo come too, but if Angelo doesn’t come to the party, then Carlo and Davide come”

Also how can I solve this one? Suppose we know that:

• “if Paolo is thin, then Carlo is not blonde or Roberta is not tall”

• “if Roberta is tall then Sandra is lovely”

• “if Sandra is lovely and Carlo is blonde then Paolo is thin”

• “Carlo is blonde”

Can we deduce that “Roberta is not tall” ?

suomynonA
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zuby
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  • What have you tried? while correlates with "and", then you have and "or" between two clauses one of which requires "and", if-then is straight forward; there should be plenty you can do; then, you can ask what you're stuck on. – amWhy Oct 02 '16 at 17:37
  • "Either ... or..." is $\lor$. "If ..., then ..." is $\to$, and so on. – Mauro ALLEGRANZA Oct 02 '16 at 17:40
  • You should be consulting your notes or text for definitions of and symbols for "or", "and" "if.....then", "not" and become accustomed to variations of these words: "and" corresponds with "but", "yet..." etc. – amWhy Oct 02 '16 at 17:45
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    There are examples of translations here and here. If you choose not to respond to my first or second comment, I will vote to close as a duplicate to one of the "here" links. You need to identify exactly which translation you are stuck on, and propose some translations, for verification of correction. We're not like a fast-food service: give order - get food(answer). – amWhy Oct 02 '16 at 18:06

1 Answers1

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Pretty straightforward:

"Angelo comes to the party while Bruno doesn’t" = "A while not B" = "A and not B" = "$A \land \lnot B"$.

"Either Carlo comes to the party, or Bruno and Davide don’t come" =

"Either C or not B and not D" = "C or (not B and not D)" = $C \lor (\lnot B \land \lnot D)$

"If Angelo and Bruno come to the party, then Carlo comes provided that Davide doesn’t come" = "If A and B then C provided not D" = "[If (A and B) then C] provided D" = "If D then [If (A and B) then C] " = $\lnot B \implies ((A \land B) \implies C)$

And so on... what more needs to be said?

fleablood
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  • Have you not read comments? Lack of effort, OP drops it off and abandons until it's answered. I don't ever want to see you insisting on effort, voting to close because of lack of effort...because you obviously thought that this question had enough quality (none) that you felt was good enough to answer. I feel sad that you're so desperate for votes or acceptances that you'll reply to any question regardless of quality or effort. – amWhy Oct 02 '16 at 18:20