Saying “if you are worried, you should get your booster” is not at all equivalent to “if you have gotten your booster, you should not be worried about this virus”.
The first statement permits that one can still be worried after having gotten one’s booster (just a little less), which the second statement does not permit. Therefore, those two statements cannot be logically equivalent.
If you had written “if you have gotten your booster, you should not be as worried about this virus [as before]”, that would have been fine.
Flag: even being less worried is an additional inference not demanded by the form of the contrapositive of “if you’re worried, you should get your booster” . But that’s just a nitpick over how literally we’re meaning logical equivalence.
I disagree that the derived statement is unreasonable. I also disagree that it’s obviously saying something other than what it literally says.
Saying “if you are worried, you should get your booster” is not at all equivalent to “if you have gotten your booster, you should not be worried about this virus”.
The first statement permits that one can still be worried after having gotten one’s booster (just a little less), which the second statement does not permit. Therefore, those two statements cannot be logically equivalent.
If you had written “if you have gotten your booster, you should not be as worried about this virus [as before]”, that would have been fine.
Flag: even being less worried is an additional inference not demanded by the form of the contrapositive of “if you’re worried, you should get your booster” . But that’s just a nitpick over how literally we’re meaning logical equivalence.