What logical conclusions will be drawn from “Set A belongs to Set B” and “Set C belongs to Set D” ?
These two propositions are independent of each other. It is clearly that no any logic law could be used to reason new conclusions from these two propositions. One wants to solve this problem, he must study the new theory base of discrete mathematics, name concept algebra at following web:
Conbra <s...@sh163.net> wrote: >What logical conclusions will be drawn from “Set A belongs to Set B” >and “Set C belongs to Set D” ?
> These two propositions are independent of each other. It is >clearly that no any logic law could be used to reason new conclusions >from these two propositions. One wants to solve this problem,
> Conbra <s...@sh163.net> wrote: > >What logical conclusions will be drawn from “Set A belongs to Set B” > >and “Set C belongs to Set D” ?
> > These two propositions are independent of each other. It is > >clearly that no any logic law could be used to reason new conclusions > >from these two propositions. One wants to solve this problem,
> What problem?
> >he must study the new theory base of discrete mathematics, name concept > >algebra at following web:
> What logical conclusions will be drawn from “Set A belongs to Set B” > and “Set C belongs to Set D” ?
> These two propositions are independent of each other. It is > clearly that no any logic law could be used to reason new conclusions > from these two propositions. One wants to solve this problem, he must > study the new theory base of discrete mathematics, name concept > algebra at following web:
> After studying concept algebra, this problem will be solved by > reader simply.
> I'd like to solve this problem at following post.
> Conbra
The propositions “Set A belongs to Set B” and “Set C belongs to Set D” are the relation of the four sets. The set A and set B in one proposition, and the set C and set D in another proposition. How to connect the relation among these four sets?
According to concept algebra the “belongs to” is one compound operation, “<”. So that these two proposition could be written as “Set A < Set B” and “Set C < Set D” using the basic operation “*” to replace “and” on concept algebra, get “Set A < Set B” * “Set C < Set D” so that the following concept equation will be got X / (Set A < Set B) * (Set C < Set D) = Dao X is unknown variable; Dao is only one constant on concept algebra. After solving this equation there are a lot of logical conclusion will be drawn. The relation among these four sets is clearly.
>> >What logical conclusions will be drawn from “Set A belongs to Set B” >> >and “Set C belongs to Set D” ?
>> >One wants to solve this problem [...]
>> What problem?
>The proplem is how to draw logical conclusions from these two >propositions?
There's no problem as it can already be done in second-order logic. Given that a set of sets is a second-order predicate, "set A belongs to B" is expressed B(A), and so "set C belongs to D" is expressed D(C). Now we can for example derive this logical conclusion:
> >> >What logical conclusions will be drawn from “Set A belongs to Set B” > >> >and “Set C belongs to Set D” ?
> >> >One wants to solve this problem [...]
> >> What problem?
> >The proplem is how to draw logical conclusions from these two > >propositions?
> There's no problem as it can already be done in second-order logic. > Given that a set of sets is a second-order predicate, "set A belongs > to B" is expressed B(A), and so "set C belongs to D" is expressed > D(C). Now we can for example derive this logical conclusion:
> On Jul 18, 4:08 pm, Conbra <s...@sh163.net> wrote:
> > What logical conclusions will be drawn from "Set A belongs to Set B" > > and "Set C belongs to Set D" ?
> > These two propositions are independent of each other. It is > > clearly that no any logic law could be used to reason new conclusions > > from these two propositions. One wants to solve this problem, he must > > study the new theory base of discrete mathematics, name concept > > algebra at following web:
> > After studying concept algebra, this problem will be solved by > > reader simply.
> > I'd like to solve this problem at following post.
> > Conbra
> The propositions "Set A belongs to Set B" and "Set C belongs to Set D" > are the relation of the four sets. The set A and set B in one > proposition, and the set C and set D in another proposition. How to > connect the relation among these four sets?
> According to concept algebra the "belongs to" is one compound > operation, "<". So that these two proposition could be written as > "Set A < Set B" and "Set C < Set D" > using the basic operation "*" to replace "and" on concept algebra, get > "Set A < Set B" * "Set C < Set D" > so that the following concept equation will be got > X / (Set A < Set B) * (Set C < Set D) = Dao > X is unknown variable; Dao is only one constant on concept algebra. > After solving this equation there are a lot of logical conclusion will > be drawn. The relation among these four sets is clearly.
> Conbra- 隐藏被引用文字 -
> - 显示引用的文字 -
X / (Set A < Set B) * (Set C < Set D) = Dao
First solution of this equation is X = (Set C < Set B) / (Set D < Set A)
The explanation of this solution in words is X = If Set D belong to Set A, then Set C also belong to Set B.
That is to say, this one conclusion could be explained as:
If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set D belong to Set A, then Set C also belong to Set B".
>> >> >What logical conclusions will be drawn from “Set A belongs to Set B” >> >> >and “Set C belongs to Set D” ?
>> >> >One wants to solve this problem [...]
>> >> What problem?
>> >The proplem is how to draw logical conclusions from these two >> >propositions?
>> There's no problem as it can already be done in second-order logic. >> Given that a set of sets is a second-order predicate, "set A belongs >> to B" is expressed B(A), and so "set C belongs to D" is expressed >> D(C). Now we can for example derive this logical conclusion:
>> The logical conclusion in step 5 is a tautology. ~Wonderer
>There is no new relation appeared at the conclusion.
Uh, you said the problem was "how to draw logical conclusions from these two propositions?" Well, I proved an answer: step 5 (above) is a logical conclusion drawn for the two propositions. But now you've switched the problem to apparently how to draw a "new relation" from the propositions. Well, I also did that, but it seems you don't know.
The logical connectives are functions (and all functions are relations). So we can drop the usual infix notation and for example instead of writing P & Q we can write &(P,Q) to make the functional (and thus relational) nature of the statement clear. So several relations were drawn from the two propositions. ~Wonderer
> On 7月19日, 上午7时59分, Conbra <s...@sh163.net> wrote:
> > On Jul 18, 4:08 pm, Conbra <s...@sh163.net> wrote:
> > > What logical conclusions will be drawn from "Set A belongs to Set B" > > > and "Set C belongs to Set D" ?
> > > These two propositions are independent of each other. It is > > > clearly that no any logic law could be used to reason new conclusions > > > from these two propositions. One wants to solve this problem, he must > > > study the new theory base of discrete mathematics, name concept > > > algebra at following web:
> > > After studying concept algebra, this problem will be solved by > > > reader simply.
> > > I'd like to solve this problem at following post.
> > > Conbra
> > The propositions "Set A belongs to Set B" and "Set C belongs to Set D" > > are the relation of the four sets. The set A and set B in one > > proposition, and the set C and set D in another proposition. How to > > connect the relation among these four sets?
> > According to concept algebra the "belongs to" is one compound > > operation, "<". So that these two proposition could be written as > > "Set A < Set B" and "Set C < Set D" > > using the basic operation "*" to replace "and" on concept algebra, get > > "Set A < Set B" * "Set C < Set D" > > so that the following concept equation will be got > > X / (Set A < Set B) * (Set C < Set D) = Dao > > X is unknown variable; Dao is only one constant on concept algebra. > > After solving this equation there are a lot of logical conclusion will > > be drawn. The relation among these four sets is clearly.
> > Conbra- 隐藏被引用文字 -
> > - 显示引用的文字 -
> X / (Set A < Set B) * (Set C < Set D) = Dao
> First solution of this equation is > X = (Set C < Set B) / (Set D < Set A)
> The explanation of this solution in words is > X = If Set D belong to Set A, then Set C also belong to Set B.
> That is to say, this one conclusion could be explained as:
> If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set > D belong to Set A, then Set C also belong to Set B".
> Above law is logical.
> Conbra- Hide quoted text -
> - Show quoted text -
X / (Set A < Set B) * (Set C < Set D) = Dao
Second solution of this equation is X = (B > C) / (A > D) The explanation of this solution in words is X = If Set A includes Set D, then Set B also includes Set C.
That is to say, this one conclusion could be explained as:
If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set A includes Set D, then Set B also includes Set C".
> > > > What logical conclusions will be drawn from "Set A belongs to Set B" > > > > and "Set C belongs to Set D" ?
> > > > These two propositions are independent of each other. It is > > > > clearly that no any logic law could be used to reason new conclusions > > > > from these two propositions. One wants to solve this problem, he must > > > > study the new theory base of discrete mathematics, name concept > > > > algebra at following web:
> > > > After studying concept algebra, this problem will be solved by > > > > reader simply.
> > > > I'd like to solve this problem at following post.
> > > > Conbra
> > > The propositions "Set A belongs to Set B" and "Set C belongs to Set D" > > > are the relation of the four sets. The set A and set B in one > > > proposition, and the set C and set D in another proposition. How to > > > connect the relation among these four sets?
> > > According to concept algebra the "belongs to" is one compound > > > operation, "<". So that these two proposition could be written as > > > "Set A < Set B" and "Set C < Set D" > > > using the basic operation "*" to replace "and" on concept algebra, get > > > "Set A < Set B" * "Set C < Set D" > > > so that the following concept equation will be got > > > X / (Set A < Set B) * (Set C < Set D) = Dao > > > X is unknown variable; Dao is only one constant on concept algebra. > > > After solving this equation there are a lot of logical conclusion will > > > be drawn. The relation among these four sets is clearly.
> > > Conbra- 隐藏被引用文字 -
> > > - 显示引用的文字 -
> > X / (Set A < Set B) * (Set C < Set D) = Dao
> > First solution of this equation is > > X = (Set C < Set B) / (Set D < Set A)
> > The explanation of this solution in words is > > X = If Set D belong to Set A, then Set C also belong to Set B.
> > That is to say, this one conclusion could be explained as:
> > If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set > > D belong to Set A, then Set C also belong to Set B".
> > Above law is logical.
> > Conbra- Hide quoted text -
> > - Show quoted text -
> X / (Set A < Set B) * (Set C < Set D) = Dao
> Second solution of this equation is > X = (B > C) / (A > D) > The explanation of this solution in words is > X = If Set A includes Set D, then Set B also includes Set C.
> That is to say, this one conclusion could be explained as:
> If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set > A includes Set D, then Set B also includes Set C".
> Above law is logical.
> Conbra- Hide quoted text -
> - Show quoted text -
X / (Set A < Set B) * (Set C < Set D) = Dao
Third solution of this equation is X = (A < D) / (B < C) The explanation of this solution in words is X = If Set B belong to Set C, then Set A also belong to Set D.
That is to say, this one conclusion could be explained as:
If "Set A belongs to Set B" and "Set C belongs to Set D"; then "if Set B belong to Set C, then Set A also belong to Set D".
