Meaning of "strong" and "weak" (formulas?) in propositional logic I was doing some review of propositional logic from Enderton's book. In one section(pg. 26 of the 2nd edition), he explains the idea that given wffs $\sigma_1, \sigma_2, \cdots, \sigma_k$ and $\tau$, one can use truth tables to check whether or not $\{ \sigma_1, \cdots, \sigma_k \} \models \tau$. Then he gives some examples of how one might in an educated way avoid checking all combinations of assignments of the propositional variables used in the sigmas and in $\tau$. This part looks o.k to me.
But then Enderton says "The stronger the antecedent(the expression on the left side), the weaker the conditional." He then gives the examples 
\begin{align}
(P \wedge Q) &\models P \\
(P \rightarrow R) &\models ((P \wedge Q) \rightarrow R) \\
(((P \wedge Q) \rightarrow R) \rightarrow S) &\models ((P \rightarrow R) \rightarrow S)
\end{align}
What does he mean by this? Which antecedent is stronger, the first or the third? Maybe a question to start out with is: what do "strong" and "weak" even mean here? Thanks for any help/clarification!
Sincerely,
Vien

I guess "$\sigma$ is stronger that $\tau$" or "$\tau$ is weaker than $\sigma$" means that $\sigma\models\tau$ but $\tau\not\models\sigma$.
First line: $(P\wedge Q)$ is stronger than $P$.
Second line: The conditional $((P\wedge Q)\rightarrow R)$ is weaker than the conditional $(P\rightarrow R)$ because the antecedent $(P\wedge Q)$ is stronger than $P$.
The third line follows from the second in much the same way as the second line follows from the first.
