Rewrite as a formal proposition

  • MHB
  • Thread starter ash1
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In summary, the conversation discusses rewriting a sentence into a formal proposition and determining its truth value using a truth table. It also mentions identifying tautologies and providing proof using logic rules. The user is advised to post their attempt at solving the problem for assistance.
  • #1
ash1
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Kindly solve for me this question with proper working.

A) Rewrite the following sentence as a formal proposition.
" If i eat apples, then i will not eat durian, and if i eat durians, then i will not eat rambutans, and if i eat rambutans, then i will not eat apples, but i will surely eat either apples, durians or rambutans.

Let G =" i eat apples", B=" i eat durians," P=" i eat rambutans".

B) Write a truth table for the proposition in (a). Is it a contradiction?

C) Which of the following are tautologies? if the statement is a tautology, give a proof using the appropriate rules of logic.(Avoid using truth tables if possible.) If it is not a tautology, then justify your answer by giving an appropriate example.

i) p(p q)
ii) ( ( p v q v r) ^ (p r) ^ (q r )) r
 
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  • #2
Hello and welcome to MHB, ash! :D

When you have a problem with which you need assistance, please to not submit it as a POTW candidate. That form is for people who have a problem that they think would make a good problem of the week, and for which they already have the solution.

So, I have moved your question here.

You will likely find the following thread to be useful:

http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/rewrite-following-sentence-formal-proposition-12846.html

For the remainder, please post what you have done so far, so our helpers know where you are stuck and can help you get past that point.
 

Related to Rewrite as a formal proposition

1. What is the purpose of rewriting as a formal proposition?

The purpose of rewriting as a formal proposition is to clearly and precisely state a hypothesis or argument in a structured and logical manner. This allows for easier testing and analysis of the proposition.

2. How do you determine the structure of a formal proposition?

The structure of a formal proposition often follows the format of "If A, then B", where A is the antecedent and B is the consequent. The antecedent represents the condition or premise, while the consequent represents the conclusion or outcome.

3. What are some key components of a formal proposition?

Some key components of a formal proposition include clear and specific language, logical and consistent structure, and testable variables. It should also be concise and avoid ambiguity or unnecessary information.

4. Can a formal proposition be proven or disproven?

Yes, a formal proposition can be proven or disproven through testing and analysis. By setting up experiments or observations that test the variables in the proposition, we can gather evidence to support or reject the proposition.

5. How is a formal proposition different from a regular statement or argument?

A formal proposition differs from a regular statement or argument in its structure and level of specificity. It follows a specific format and uses precise language to clearly state a hypothesis or argument, while a regular statement or argument may be more informal and open to interpretation.

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