How do I remember Implication Logic $(P \to Q)$ in simple English?
I read some sentence like
- If $P$ then $Q$.
- $P$ only if $Q$.
- $Q$ if $P$.
But I am unable to correlate these sentences with the following logic.
Even though the truth table is very simple, I don't want to remember it without knowing its actual meaning.
$$\begin{array}{ |c | c || c | }
\hline
P & Q & P\Rightarrow Q \\ \hline
\text T & \text T & \text T \\
\text T & \text F & \text F \\
\text F & \text T & \text T \\
\text F & \text F & \text T \\ \hline
\end{array}$$
Best Answer
If you start out with a false premise, then, as far as implication is concerned, you are free to conclude anything. (This corresponds to the fact that, when $P$ is false, the implication $P \rightarrow Q$ is true no matter what $Q$ is.)
If you start out with a true premise, then the implication should be true only when the conclusion is also true. (This corresponds to the fact that, when $P$ is true, the truth of the implication is the same as the truth of $Q$.)