This is lesson 6/16 in the Advanced Logic Section. On DeMorgans law. Question 1. Translate the sentence into logic.
"Unless the leather is soaked and tanned for 3 days, the resulting boot will be smelly."
The right answer is
/S or /T ---> BS
contrap: /BS ---> S & T
Why does it turn from an “and” to an “or” statement if you choose /S & /T as the sufficient condition?
I thought that for “unless” conditionals, you just pick one statement and negate it and that’s the sufficient.
I’m choosing S & T as the sufficient, and BS as the necessary.
so
/S & /T —> BS
If the leather isn’t soaked and tanned, the boot will be smelly.
so the contrapositive would be…
/BS –> S or T
If the boot isn’t smelly, the leather was soaked or tanned.
I see that I’m wrong but I don’t understand why.
Is it just..whenever an & statement is negated, it turns into an or statement? and whenever an or statement is negated it turns into an & statement?
I’m super confused bc now I’m looking at the contrapositive of #2 on that quiz and it’s /S & /H —> E or D
If "and" statements turn into "or" statements when they’re negated then why isn’t that the case here >.<
P.S. I do know the splitting rules it's just hard to type onto here so I left it without splits.
