[Logic] Symbolizing Sentences

[@valeriobertoncello1809]

6:17 Shouldn't "unless" be the same as XOR, and not just OR?

[@luizg8034]

To clarify
+: and
×: or
~: not
->: implies
O: I go outside
R: it rains
O × R is false iff ~O + ~R
O × R is also equivalent to
~O -> R,
or (strict 'or', both cannot be true) to
~R -> O.
Both implications are equivalent to
~O + ~R.
Now, ~R -> O is true if R is true or O is true, or both, and is false if R is false and O is false. This means it's equivalent to R × O.
"I will go outside unless it rains" is true if it rains and I stay, and it's false if it rains and I go. If it doesn't rain, it's true if I go and if I stay...?
It's debatable, but if it's false, the sentence would not be equivalent to
O × R, but to
O ~R (which is true when O and R have identical truth values: both true or both false), the same thing as R ~O

[@canonlaw3929]

Very good stuff-thanks!

[@justus4684]

6:33
Couldn't you also state it as:
"I will not go outside if and only if it is not raining"?

[@gayatrighosh2034]

Thank you so much 💙💙💙💙

[@lucasjanine2000]

Thank you.

[@SeekingUltimateSynthesis]

Why wouldn't the unless example become : o ~r

[@gayatrighosh2034]

Hey can you help me??
Pls symbolize
"We shall swim even if it rains" .. Please help me

[@TheFearlocator]

I think in the sentence "Mary or Ronald will win the rase", it should be "(M and notR) or (notM and R)"
Because it's either Mary or Ronald, they cannot both win the race.