The meaning of Implication in Logic 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.
$$\begin{array}{ |c | c || c | }
  \hline
  P & Q & P\Rightarrow Q \\ \hline
  \text T & \text T & \text T \\
  \text T & \text F & \text F \\
  \text F & \text T & \text T \\
  \text F & \text F & \text T \\ \hline
\end{array}$$

*

*If $P$ then $Q$ is equivalent to $P\to Q$

*$P$ only if $Q$ is also equivalent to $P\to Q$ (See example here)

*$Q$ if $P$ is same as if $P$ then $Q$ and equivalent to $P\to Q$
However, note (following statement which is not given in the original question): $P$ if $Q$ is equivalent to if $Q$ then $P$ or $Q\to P$
