Biconditionals and Conjunctions in Truth Tables Given that a biconditional $p\iff q$ is True what can be concluded from the statement $\lnot p\land \lnot q$?
In a worded example:
I wear my running shoes if and only if I exercise. (True)
I am not exercising AND I am not wearing my running shoes. (?)
If we set up a truth table, the biconditional is True in two of the four occurrences, but we see that $\lnot p\land \lnot q$ is both True and False, which would mean there is no conclusion, correct?

Restating Ryan G's answer, which I completely agree with:
Given $P \iff Q$ you know that there are only two possibilities:
Possibility (1) : $P \wedge Q$.
Possibility (2) : $(\neg P) \wedge (\neg Q).$
Since the only information available is that the  biconditional is true, there is no way of determining which of Possibility (1) or Possibility (2) pertains.
