I don't get the sushi example, if I say that someone eats sushi doesn't it mean that this someone eats at least one kind of sushi and not necessarily all kinds of sushi? why use "∀y[Sy →Exy]" instead of "∃y[Sy∧Exy]" ?
Hi Trev, thank you so much for making this vid! Could you explain how to translate this into predicate logic: A stamp collector wants to include in her collection exactly one stamp from each country of Africa. If I(s) means that she has stamp s in her collection, F(s, c) means that stamp s was issued by country c, the domain for s is all stamps, and the domain for c is all countries of Africa, express the statement that her collection satisfies her requirement. (Do not use Ǝ! symbol)
why we didn't add for all x x is a cake for previous examples but we did it for sushi. If food names were considered generic then we had to do it for cake and pie too.
You can define sushi however you like. The variables themselves don't really matter, it's more a convention to translate them back and forth. You still need to explicitly define all sushi just as you defined all friends, and you need to verify that it is sushi just as in the previous examples you verified that D(x) was a dog. You have to verify that s is S(s) or sushi in this case. He avoids using s because it can get confusing very fast just as when you're doing calculus you avoid using d as a variable because you don't want to use dd for derivatives.
That's not necessary because conjunction is associative and commutative. A : "I eat apples" B: "I love biking" G: "I go to the gym" Commutative: A^B^G : "I eat apples, love biking and go to the gym." G^B^A : "I go to the gym, love biking, and eat apples." Associative: A*(B*G): "I eat apples. I also love biking and go to the gym." (A*B)*G: "I eat apples and love biking. I Also go to the gym."
How would express something like 'If John claims that all dogs are happy then all dogs are happy'? Seems like 'all dogs are happy' would have to both be treated as an object and a proposition? Isn't clear how you can express that using the notation of predicate logic?
Warning, it has been a long time since I took a logic class, so take this with a grain of salt. I think you would not prefer to do this because "Solomon and Kevin are both dogs" is not atomic. You can talk about the doglliness of both Solomon and Kevin independently and, if we want to use that statement as a premise, we would write them independently and join them together with an '&'. This contrasts the comparison examples because I can't describe the relative happiness of one person unless I am directly referencing someone else (or a different benchmark).
I think you made a mistake on the 6th example at 24:25. I think the correct answer is ∃x[kid(x) ∧ ∃y[fred(y) ∧ made_fun_of(x, y)] ∧ ∃z[teacher(z) ∧ ate(x, z)]]
Can I just say how much of a life saver you are? Concepts explained crystal clear, unlike my professor. Thank you so much!
This video was so helpful.. Thank you so much :))
thankyou so much trev . descrete mathematics was nightmare for me until i found your channel thank you so much.
I don't get the sushi example, if I say that someone eats sushi doesn't it mean that this someone eats at least one kind of sushi and not necessarily all kinds of sushi? why use "∀y[Sy →Exy]" instead of "∃y[Sy∧Exy]" ?
Was looking to see if anyone else realized this.
I think you are right.
Hi Trev, thank you so much for making this vid! Could you explain how to translate this into predicate logic: A stamp collector wants to include in her collection exactly one stamp from each country of Africa. If I(s) means that she has stamp s in her collection, F(s, c) means that stamp s was issued by country c, the domain for s is all stamps, and the domain for c is all countries of Africa, express the statement that her collection satisfies her requirement. (Do not use Ǝ! symbol)
Hey here's how I thought of ot for all s f(s,c)->i(s)
Wow men ! you save my semester
Thx alot 🙏
thanks trev
why we didn't add for all x x is a cake for previous examples but we did it for sushi. If food names were considered generic then we had to do it for cake and pie too.
For question 5, if you define s as Sushi, could you not write Ax(Fx ^ Exs -> Tx)
that's what I thought as well, @trevtutor what do you think ???
I think the same.
You can define sushi however you like. The variables themselves don't really matter, it's more a convention to translate them back and forth. You still need to explicitly define all sushi just as you defined all friends, and you need to verify that it is sushi just as in the previous examples you verified that D(x) was a dog. You have to verify that s is S(s) or sushi in this case. He avoids using s because it can get confusing very fast just as when you're doing calculus you avoid using d as a variable because you don't want to use dd for derivatives.
I would say no because 'sushi' in that statement is referring to anything that is sushi, not just a specific bit of individual sushi.
Same here a bit confusing
very helpful, just wanted to say there’s a mistake at 18:22, you didn’t demonstrate what is the main conjunction, whether it’s the first or the second
same mistake on 24:30
That's not necessary because conjunction is associative and commutative.
A : "I eat apples"
B: "I love biking"
G: "I go to the gym"
Commutative:
A^B^G : "I eat apples, love biking and go to the gym."
G^B^A : "I go to the gym, love biking, and eat apples."
Associative:
A*(B*G): "I eat apples. I also love biking and go to the gym."
(A*B)*G: "I eat apples and love biking. I Also go to the gym."
this is so helpful. thank you so much!!
Can anyone translate ‘I made you happy’?
Do you have smt harder in english like you lear basic things like this or ?
This was very helpful!!
Thank you!
Thank you Trev
thx, this is helpful
dude you are awesome!
your tools are awesome sir ,which tool are you using sir?
thank you so much!!
How would express something like 'If John claims that all dogs are happy then all dogs are happy'?
Seems like 'all dogs are happy' would have to both be treated as an object and a proposition? Isn't clear how you can express that using the notation of predicate logic?
The sushi example feels needlessly complicated. Why not just go with (Fx ^ Sx) where the S means "eats sushi", treating it as a property of x instead.
I am a little confused on when to use and and when to use arrow
Thanks a lot
Who's here before giving their CST exam ?
Me for this years 🤣
for somme dog is happy we can interjection..so the sample symbol from pevious exampple
Great videos, but why is "all sushi" in the example 5, if one eats sushi, should he have to eat all sushi?
just because I eat pizza doesn't mean I eat Pizza with meat on it because I'm vegetarian
thank you. i want to askeone question. What does Lambda means in translation of predicate logic?
This is me before watching the video: Wtf is thiss
(Edit after watching) eh ok
But, Still fked
Thank you very helpful
For the sentence "Solomon and Kevin are both dogs", would D(s, k) also work or not?
Warning, it has been a long time since I took a logic class, so take this with a grain of salt.
I think you would not prefer to do this because "Solomon and Kevin are both dogs" is not atomic. You can talk about the doglliness of both Solomon and Kevin independently and, if we want to use that statement as a premise, we would write them independently and join them together with an '&'.
This contrasts the comparison examples because I can't describe the relative happiness of one person unless I am directly referencing someone else (or a different benchmark).
No, how would you define the predicate as? D (x, y) : x and y are both dogs? We need to split this into independent Predicates.
thank you, thank you so much. UwU
yesssssssssssss
my frnd abu amara thinks ur answer is wrong in 'A kid question' ????/?????
So with the second example, with Solomon and Kevin is a dog , can you write it like this? D(S and k)
nope
How "Every monster is scary" and "Every dog is happy" is any different? So why one is using arrow and the other is using 'and'
They both use the arrow. The example at 9:36 shows the "and" does NOT work.
@@Trevtutor My bad. I misunderstood. Thanks for the reply.
Who's here for Erdal teacher's exam?
"If girls has husband then she is married " please translate these , anyone please
Ex(G(x)+H(x)=M(x)
It is similar to 5th example. ForAllX[[Gx & ForSomeY [Hyx]] => Mx]
Where Gx : x is a girl
Hyx : y is husband of x
Mx : x is married
Here in time for farons quiz
I think you made a mistake on the 6th example at 24:25. I think the correct answer is ∃x[kid(x) ∧ ∃y[fred(y) ∧ made_fun_of(x, y)] ∧ ∃z[teacher(z) ∧ ate(x, z)]]
We don’t assign variables to proper names. They behave as constants. So Fred(y) doesn’t really make sense.