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Related Discussions
Quiz 1 on Complex Conditional Translations to Lawgic
_oshun1_
Alum Member
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.
"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.
Comments
Let's break the sentence down a bit:
first condition: (S and T) are a package deal because they represent an entire condition (sufficient or necessary). If it helps, think of "(S and T)" as "X" instead
second condition: BS
logical indicator: unless (grp 3, negate sufficient)
thus, the sentence reads as "unless X, BS", which translates to /X->BS or /(S and T)->BS
applying De Morgan's law to "/(S and T)", we get "/S or /T".
Thus, the translation simplifies to (/S or /T)->BS
and the contrapositive is /BS->/(/S or /T) and further /BS->(S and T)
Regarding question #2, the translation of the original sentence is (E or D)->(S or H). Taking a more simplistic approach, we could say "(E or D)" is represented by "A" and "(S or H)" is represented by "B". Thus, A->B. Clearly, the contrapositive of A->B is /B->/A and thus /(S or H)->/(E or D).
Applying De Morgan's law, we get (/S and /H)->(/E and /D).
So remember that when you negate the sufficient or necessary condition, you are first negating the entire condition and then applying De Morgan's law. De Morgan's law is triggered by the negation of the entire condition containing "and" or "or".
Hope that helps!