I'm struggling understanding truth tables.
Let's denote a true proposition by 1 and a false proposition by 0.
We will be considering the propositional
operation, $\Rightarrow$ (implies).
The truth table looks like the following
\begin{array}{c|cc}\rightarrow & 0 & 1\\\hline\\0 & 1 & 1\\1 & 0 & 1\end{array}
Does this say that $(0 \land 0) \rightarrow 1$?
If it does, what exactly does that mean — are we looking at $(0\rightarrow0)$ as one proposition and saying it is true?
Can you please explain this in english — using sentences like (x>5 for propositions instead of just writing $P$ or $Q$ for propositions)
EDIT
Best Answer
What you've posted is the truth table for material implication (the conditional) $p \rightarrow q$.
EDIT:
To better understand the material conditional (the connective $\rightarrow$, i.e. implication), see the following posts:
At each of those links, you'll find more linked questions that are also relevant. You are not alone: logical implication (e.g. $p\rightarrow q$) is perhaps the most difficult connective to grasp, in terms of its truth-table and how it is defined, in classical logic, (which is, in part, explained by the fact that in natural language, the term "implies" is used in ways whose meaning is not captured by its narrower meaning, as defined in logic).
If you have any further questions, I'll be happy to try and answer them!