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I am going over the first chapter of Velleman's How to Prove It. I have never studied logic before and while I understand most of what is happening, I am not sure that I am understanding how to transform sentences into symbols that can be tested. One of the exercises asks: Identify thepremisesandconclusionand determine if the following argument a valid one?

Jane and Pete won't both win the math prize. Pete will win either the math prize or the chemistry prize. Jane will win he math prize. Therefore Pete will win the chemistry prize.

2. Relevant equations

A valid argument is one in which the premises cannot all be true without the conclusion being trues as well

3. The attempt at a solution

I have identified thepremisesto be:

1.)"Jane and Pete won't both win the math prize",

2.)"Pete will win either the math prize or the chemistry prize",

3.)"Jane will win the math prize."

and theconclusionto be:

"Pete will win the chemistry prise."

Are my premises correct? Or should I have not listed (1) and (2) separately? That is, should I have combined them to say:

"Jane and Pete won't both win the math prize AND Pete will win either the math prize or the chemistry prize"??

In order to test the validity, I need to construct a truth table.

I have translated my premises symbolically as follows:

Define the follwing symbols:

P: Pete will win the math prize

J: Jane will win the math prize

P': Pete will win the chemistry prize

##\lnot(P \land J)\land(P \lor P')##

##J##

##\therefore P'##

Now for the truth table:

[tex]

\begin{array}{l c l}

PJP' & [\lnot(P \land J)\land(P \lor P')] & P' \\

---&------&---\\

TTT & F & T \\

TTF & F & F \\

TFF & T & F \\

\dots & &

\end{array}

[/tex]

I can already see that I am doing something wrong here. The last row has that my premise is true, but the conclusion is false, however, I know from the solution that the argument is valid. So where am I going wrong?

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# Homework Help: Sentential Logic: Is the argument valid?

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