Sorry if this is overly simple but I've never actually done a logic course beyond truth tables. I can guess the meaning but I've never encountered this one.

If I have the statement $\displaystyle X \Leftrightarrow Y \Leftrightarrow Z$ is this just a shorthand way of writing the three statements $\displaystyle X \Leftrightarrow Y$, $\displaystyle Y \Leftrightarrow Z$, and $\displaystyle X \Leftrightarrow Z$?

I can give you the actual problem statement if you need it.

Thanks!

-Dan

2. ## Re: Linked iff statements

Originally Posted by topsquark
Sorry if this is overly simple but I've never actually done a logic course beyond truth tables. I can guess the meaning but I've never encountered this one. If I have the statement $\displaystyle X \Leftrightarrow Y \Leftrightarrow Z$ is this just a shorthand way of writing the three statements $\displaystyle X \Leftrightarrow Y$, $\displaystyle Y \Leftrightarrow Z$, and $\displaystyle X \Leftrightarrow Z$?
The statement that $X\iff Y$ means that $X$ is true if and only if $Y$ is true.
That is in a truth table the truth values are the same: SEE HERE
Please note the last line $F~F~\to T$ that is having the same truth value is true.
Thus then $\iff$ is transitive.

3. ## Re: Linked iff statements

Originally Posted by Plato
The statement that $X\iff Y$ means that $X$ is true if and only if $Y$ is true.
That is in a truth table the truth values are the same: SEE HERE
Please note the last line $F~F~\to T$ that is having the same truth value is true.
Thus then $\iff$ is transitive.
Okay, thanks. Just checking.

-Dan

4. ## Re: Linked iff statements

I tried using a truth table to prove the transitive property. Does the implication in column 8 show that?

I'm convinced it does but I'd just like a second eye. This table shows that for all possible truth values of X, Y, and Z, the statement if (X iff Y)^(Y iff Z) then (X iff Z) is a tautology -- that is (X iff Y)^(Y iff Z) is equivalent to (X iff Z).