propositions and logic help

Hi

I am having trouble understanding some subjects in maths, and seem unable to find similar examples elsewhere. I do not want to cheat, nor do this without understanding how it works, so I am hoping that someone can give me some ideas to help me figure this one out alone.

The question is:

if P then Q
if not R then not Q
P or R
Therefore, R.

I need to create a truth table or "any other method that works" to show that this argument is valid.

It may be a big ask, but I would really appreciate it if no one writes an answer so much as perhaps put this into a sentence so I may better understand it. As an example:

P= Eat your vegetables
Q= You will get dessert

I am not sure how R fits into this proposition, any help greatly appreciated!!

Also how/where can I get software or fonts which allow me to type the proper symbols and create tables so I can do this on my PC? Thanks!

Quote:

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Originally Posted by starlaughter

Also how/where can I get software or fonts which allow me to type the proper symbols and create tables so I can do this on my PC? Thanks!

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No software necessary. Learn to enter LaTex code into your questions.
http://www.mathhelpforum.com/math-he...-tutorial.html

starlaughter,

I have found the following video helpful:

YouTube - Lecture 1 - Propositional Logic

Best wishes!

Hello starlaughter

Quote:

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Originally Posted by starlaughter

Hi

I am having trouble understanding some subjects in maths, and seem unable to find similar examples elsewhere. I do not want to cheat, nor do this without understanding how it works, so I am hoping that someone can give me some ideas to help me figure this one out alone.

The question is:

if P then Q
if not R then not Q
P or R
Therefore, R.

I need to create a truth table or "any other method that works" to show that this argument is valid.

It may be a big ask, but I would really appreciate it if no one writes an answer so much as perhaps put this into a sentence so I may better understand it. As an example:

P= Eat your vegetables
Q= You will get dessert

I am not sure how R fits into this proposition, any help greatly appreciated!!

Also how/where can I get software or fonts which allow me to type the proper symbols and create tables so I can do this on my PC? Thanks!

---

The expression you need to evaluate in your truth table is:

$\displaystyle ((P \Rightarrow Q) \wedge (\neg R \Rightarrow \neg Q) \wedge (P \vee R)) \Rightarrow R$

and you'll need to show that the expression evaluates to True in every row of the table. If you're not sure how to do it, you may find the notes I've put on Wikibooks helpful. You'll find them at Discrete mathematics/Logic - Wikibooks, collection of open-content textbooks, where there are quite a few worked examples, exercises and answers.

As far as your illustration with the veg and dessert is concerned, you'll need a further statement for R (and you'll also need to make P a proposition, which it currently isn't!). How about:

P is "You eat your vegetables"
Q is "You will get dessert"
R is "You have good table manners"

Then:

$\displaystyle P \Rightarrow Q$ is "If you eat your vegetables, you will get dessert"

$\displaystyle \neg R \Rightarrow \neg Q$ is "If you do not have good table manners, then you will not get dessert"

$\displaystyle P \vee R$ is "You eat your vegetables or you have good table manners (or both)"

Taken together, we have to show why these three propositions mean that $\displaystyle R$ is true: You have good table manners.

Why is this so? Well, suppose $\displaystyle R$ is false - in other words, you don't have good table manners. Then $\displaystyle (P \vee R)$ can only be true if you eat your vegetables.

But if you eat your vegetables, you will get dessert, $\displaystyle (P \Rightarrow Q)$. But you won't get dessert if you don't have good table manners $\displaystyle (\neg R \Rightarrow \neg Q)$. Therefore you must have good table manners.

This contradicts the original assumption. So you do have good table manners after all. (Good for you!)

Grandad

Thank you all so much, this has been very helpful and very much appreciated!
(Clapping)