What does it mean to "strengthen the precondition and weaken the postcondition" in Hoare logic?
Condition&nbsp;$A$ is stronger than condition&nbsp;$B$ if $A$ implies&nbsp;$B$.  That is, if $B$&nbsp;holds in all situations in which $A$&nbsp;holds.  Conversely, if $A$ is stronger than&nbsp;$B$, then $B$ is weaker than&nbsp;$A$. Note that, from the definition, $A$&nbsp;is stronger and weaker than itself, since $A$ implies&nbsp;$A$.  (We might prefer to say "at least as strong as" instead of "stronger than" but I guess that gets convoluted and it's easier to just remember that "stronger than" really means "at least as strong as".)

So, to strengthen a condition is to replace it with a stronger one; to weaken a condition is to replace it with a weaker on. Because a condition is always stronger and weaker than itself, the phrase "strengthen the precondition and weaken the postcondition" does indeed mean that we can leave one (or even both!) of them unchanged.