# Thread: How would I do this truth table?

1. ## How would I do this truth table?

How would I draw out the truth table for something with 3 things? (p, q and r). I am only used to doing 2 things (p and q) Here are the two things that I am supposed to check whether or not they are logically equivalent.

P = (p --> q) ^ (q --> r), Q = p --> r

All I need to know is how to set up the truth table, I can do the calculations myself.

2. ## Re: How would I do this truth table?

Originally Posted by kmjt
How would I draw out the truth table for something with 3 things? (p, q and r). I am only used to doing 2 things (p and q) Here are the two things that I am supposed to check whether or not they are logically equivalent.
P = (p --> q) ^ (q --> r), Q = p --> r
All I need to know is how to set up the truth table, I can do the calculations myself.
Have a look at this.

3. ## Re: How would I do this truth table?

Hello, kmjt!

How would I draw out the truth table for something with 3 things?

. . $\displaystyle \big[(p \to q) \wedge (q \to r)\big] \;\to\; (p \to r)$

. . $\displaystyle \begin{array}{|c|c|c||c|} p&q&r& \big[(p \to q) \wedge (q\to r)\big] \:\to\:(p \to r) \\ \hline T&T&T& \\ T&T&F& \\ T&F&T& \\ T&F&F& \\ F&T&T& \\ F&T&F& \\ F&F&T& \\ F&F&F& \\ \hline \end{array}$

4. ## Re: How would I do this truth table?

As another hint: p -> q == ~p v q

5. ## Re: How would I do this truth table?

Originally Posted by CaramelCardinal
As another hint: p -> q == ~p v q
What does "==" mean?
If it means "if and only if" then please learn to use LaTeX notation.
For example [TEX]\left( {p \Rightarrow q} \right) \Leftrightarrow \left( {\neg p \vee q} \right)[/TEX] gives $\displaystyle \left( {p \Rightarrow q} \right) \Leftrightarrow \left( {\neg p \vee q} \right)$.

Do you see why that is so much easier to read?
Why that is so much more professional?
Why that is then so much more helpful?

6. ## Re: How would I do this truth table?

I already figured this out, thanks again Plato!