I wanted to share an example I used to illustrate the concept:
M -> N and O
I imagined M being "meal", and N being "noodles" and "O" onions. It is necessary to have noodles and onions to make a tasty pasta meal.
Clearly, if you're out of noodles, you can't make pasta, and if you're out of onions, it might turn out rather flavourless (not a meal). This logic translates pretty cleanly into:
If "and" is on the necessary side for the example if M is adopted then O and N are adopted, and we draw it with two arrows pointing from M does it still mean that if M is adopted then both O and N are adopted? Or since the can be shown as two different arrows pointing from M that means at if M is adopted then at least one of them is also adopted?
Personally I needed to see all 4 variations of conjunctions and disjunctions in their contrapostive form (using Morgan's law of course) before it become clear. Hopefully this helps others.
IF there is a thing called De Morgan's Law, THEN it would help me to learn the contrapositive of conjunctions AND the contrapositive of disjunctions.
Contrapositive:
IF a thing could not help me learn the contrapositive of conjunctions OR the contrapositive of disjunctions, THEN this thing is not called De Morgan's Law.
is the rule still valid if the conjunction or disjunction were swapped in the conditional argument? In the example, the conjunction is in the necessary. Would the law be applied differently if it were in the sufficient
Hi! For logical equivalence questions, is an argument's contrapositive considered logically equivalent to the argument? For example, If Adam likes apples and also likes dessert, he will like apple pie. A and D --> AP . If a question is asking which of the following sentences follows the same logic structure and this is an answer choice, would it be correct?: If Samantha does not like car shows and she also does not like rain, she will definitely not go to the car show this Saturday. /C and /R ---> /SC
I am struggling to find the value in these types of lesson knowing that we will just not have time to do all of those s* on the exam... I understand that you are only supposed to use these techniques on really confusing questions, but we are spending so much time on these concepts
#feedback #help it would be really helpful if we could step back and set general rules rather than solely run through than examples (their english translations can overcomplicate things) for some of these. i wrote a simple A, B, C lawgic example (without any english translation), but want to make sure it's correct.
negating conjunctions:
A and B ⟶ C
/C ⟶ /A or /B
negating disjunctions:
A⟶ B or C
/B and /C ⟶ /A
can you let me know if this is right, or if there are any errors here?
#help #feedback "if N or O is not adopted, then M cannot be adopted" What is this statement's contrapositive in English? I.e., what is M → N and O's application in English? Does it mean that if M was adopted then both N and O were adopted? Are we reading the "or" in the first statement as "and" or inclusive "or"?
Let me know if I am incorrect in doing so but I kind of separated the process and made it longer to help myself better understand. Meaning in my head I thought of De Morgan's law as being the "negate" part of the contrapositive process "flip and negate". Flipping the conditions is the first step, and then to negate using De Morgan's law is the second step. I still ended up with the same answers. Not sure if this was obvious to everyone else but going about the process in this way helped me understand better.
Negate a Conjunction
Initial conditional statement:
M→N and O
↳flip the two conditions:
(N and O) → M
↳conjunction (and) swapped for the disjunction (or):
(N or O)→M
↳ Negate each the conjuncts:
/N or /O→/M
Negate a Disjunction
Initial conditional statement:
/N or /O→/M
↳flip the two conditions:
/M→/N or /O
↳ disjunction (or) swapped for the conjunction (and):
So it says that the contrapositive of /N or /O > /M is M > O and N.
When I think of this with a real example it doesn't make sense to me.
So for example: if you don't eat well or you don't exercise then you can't be in shape. The contrapositive according the the rule would be if you are in shape then you must exercise and eat well. Using my common sense though I would think of it as If you are in shape then you must exercise or eat well.
It does not seem like you negate when doing disjunctions. Is it flipped when the section is at how to negate a disjunction or do you flip for each scenario?
That's a lot of /'s but don't worry, remember that negations cancel out. To distribute the / into the parenthesis, obey De Morgan: to negate a disjunction, swap the "or" (disjunction) for an "and" (conjunction) and negate each of the disjuncts:
N and O
Put it together:
M → N and O
Thank you Augustus De Morgan and may you rest in peace."
HOWEVER WOULDN'T IT BE: N AND O --> /M ... seems as if they forgot to fully finish negating and entirely did not flip
dude is this even going to be on the test? Like is this part of the foundations course a waste of my time right now if the logic games are gone starting this month? I'm toiling over understanding these formulas and then I go and take a practice test and none of it seems applicable. Help am I crazy or not seeing how this should be helping me / has helped me with the post august test? It feels like my time would be way better spent on logical reasoning and RC practice/ sections. Please share your thoughts / strategies with me I don't really know what to do
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85 comments
If Cain runs he will go to the store and the movies .
Runs → store and movies
The negation
/ store or / movies → /run
If Cain did not go to the store or the movies then he did not run.
for the example provided in the lecture video, could I also say:
/N -> /O and /M
or
/O -> /N and /M
I understand the concept but I was curious as to whether these would be considered incorrect?
Is it necessary to do the conjunction step? Or can we just put it into lawgic and move on.
I wanted to share an example I used to illustrate the concept:
M -> N and O
I imagined M being "meal", and N being "noodles" and "O" onions. It is necessary to have noodles and onions to make a tasty pasta meal.
Clearly, if you're out of noodles, you can't make pasta, and if you're out of onions, it might turn out rather flavourless (not a meal). This logic translates pretty cleanly into:
/N or /O -> /M
Let me know if this helped anyone else!
If "and" is on the necessary side for the example if M is adopted then O and N are adopted, and we draw it with two arrows pointing from M does it still mean that if M is adopted then both O and N are adopted? Or since the can be shown as two different arrows pointing from M that means at if M is adopted then at least one of them is also adopted?
Conjunction/Disjunction vs Contrapostive
A AND B → C
/C → /A OR /B (Contrapostive Morgan's Law)
A OR B → C
/C → /A AND /B (Contrapostive Morgan's Law)
A → B AND C
/B OR /C → /A (Contrapostive Morgan's Law)
A → B OR C
/B AND /C → /A (Contrapostive Morgan's Law)
Personally I needed to see all 4 variations of conjunctions and disjunctions in their contrapostive form (using Morgan's law of course) before it become clear. Hopefully this helps others.
mah boy augustus
IF there is a thing called De Morgan's Law, THEN it would help me to learn the contrapositive of conjunctions AND the contrapositive of disjunctions.
Contrapositive:
IF a thing could not help me learn the contrapositive of conjunctions OR the contrapositive of disjunctions, THEN this thing is not called De Morgan's Law.
is the rule still valid if the conjunction or disjunction were swapped in the conditional argument? In the example, the conjunction is in the necessary. Would the law be applied differently if it were in the sufficient
Hi! For logical equivalence questions, is an argument's contrapositive considered logically equivalent to the argument? For example, If Adam likes apples and also likes dessert, he will like apple pie. A and D --> AP . If a question is asking which of the following sentences follows the same logic structure and this is an answer choice, would it be correct?: If Samantha does not like car shows and she also does not like rain, she will definitely not go to the car show this Saturday. /C and /R ---> /SC
I am struggling to find the value in these types of lesson knowing that we will just not have time to do all of those s* on the exam... I understand that you are only supposed to use these techniques on really confusing questions, but we are spending so much time on these concepts
#feedback #help it would be really helpful if we could step back and set general rules rather than solely run through than examples (their english translations can overcomplicate things) for some of these. i wrote a simple A, B, C lawgic example (without any english translation), but want to make sure it's correct.
negating conjunctions:
A and B ⟶ C
/C ⟶ /A or /B
negating disjunctions:
A⟶ B or C
/B and /C ⟶ /A
can you let me know if this is right, or if there are any errors here?
#help #feedback "if N or O is not adopted, then M cannot be adopted" What is this statement's contrapositive in English? I.e., what is M → N and O's application in English? Does it mean that if M was adopted then both N and O were adopted? Are we reading the "or" in the first statement as "and" or inclusive "or"?
is the phrase /A or /B --> C the same as /(A or B) -->C???
same question for "and" function: would /A and /B --> C be the same as /(A and B) --> C
Let me know if I am incorrect in doing so but I kind of separated the process and made it longer to help myself better understand. Meaning in my head I thought of De Morgan's law as being the "negate" part of the contrapositive process "flip and negate". Flipping the conditions is the first step, and then to negate using De Morgan's law is the second step. I still ended up with the same answers. Not sure if this was obvious to everyone else but going about the process in this way helped me understand better.
Negate a Conjunction
Initial conditional statement:
M→N and O
↳flip the two conditions:
(N and O) → M
↳conjunction (and) swapped for the disjunction (or):
(N or O)→M
↳ Negate each the conjuncts:
/N or /O→/M
Negate a Disjunction
Initial conditional statement:
/N or /O→/M
↳flip the two conditions:
/M→/N or /O
↳ disjunction (or) swapped for the conjunction (and):
/M→/N and /O
↳ Negate each the disjuncts:
M→N and O
Why even switch AND to OR? Doesn't the contrapositive also work if you say that "If you don't have A AND you don't have B, you can't have C"?
So it says that the contrapositive of /N or /O > /M is M > O and N.
When I think of this with a real example it doesn't make sense to me.
So for example: if you don't eat well or you don't exercise then you can't be in shape. The contrapositive according the the rule would be if you are in shape then you must exercise and eat well. Using my common sense though I would think of it as If you are in shape then you must exercise or eat well.
Where am I going wrong here?
#feedback Will we see conjunction and disjunction represented ever without "and" or "or".
or is this simply not possible to represent in the English language, lol.
It does not seem like you negate when doing disjunctions. Is it flipped when the section is at how to negate a disjunction or do you flip for each scenario?
Old Captain DeMorgan. Introduced to him when I was in the Navy.
If I’m understanding correctly to negate a conjunction : M -> N and O - we flip, negate + change the and to or leaving us with : / N or / O -> /M
To negate a disjunction: /N or /O -> /M
we flip, negate + change or to and
leaving us with : M -> N and O
#help
So negating disjunctions, no flip right? Just negate?
Just making sure I got the disjunction part correct...
J → A or B
becomes
/A and / B → /J
#feedback
curriculum states:
How to negate a disjunction
First, we "flip and negate:"
M → /(/N or /O)
That's a lot of /'s but don't worry, remember that negations cancel out. To distribute the / into the parenthesis, obey De Morgan: to negate a disjunction, swap the "or" (disjunction) for an "and" (conjunction) and negate each of the disjuncts:
N and O
Put it together:
M → N and O
Thank you Augustus De Morgan and may you rest in peace."
HOWEVER WOULDN'T IT BE: N AND O --> /M ... seems as if they forgot to fully finish negating and entirely did not flip
dude is this even going to be on the test? Like is this part of the foundations course a waste of my time right now if the logic games are gone starting this month? I'm toiling over understanding these formulas and then I go and take a practice test and none of it seems applicable. Help am I crazy or not seeing how this should be helping me / has helped me with the post august test? It feels like my time would be way better spent on logical reasoning and RC practice/ sections. Please share your thoughts / strategies with me I don't really know what to do