MHB Rewrite as a formal proposition

[ash1]

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

 

[MarkFL]

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.