combantorics: set {0, 1, 2, 3) is given; only operation on the set is addition.

shahar

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The set {0, 1, 2, 3) is given. The only operation on the set is addition.

ff the result of the addition operation is one items of the set, it called internal result,
else it called external result.

The number of exercises with internal result is 4
The number of external result is 6.

How I represent it by representation of combinatorics:
(1) The number exercises of internal result?
(2) The number exercises of external result?
(3) The number of exercises that are derive by commutative law?
 
Last edited:
The set {0, 1, 2, 3) is given. The only operation on the set is addition.

ff the result of the addition operation is one items of the set, it called internal result,
else it called external result.

The number of exercises with internal result is 4
The number of external result is 6.

How I represent it by representation of combinatorics:
(1) The number exercises of internal result?
(2) The number exercises of external result?
(3) The number of exercises that are derive by commutative law?

The problem needs a lot of clarification.

What does "exercise" mean? If you mean "sum" (that is, the sum of two numbers in the set), there are 16 of those, not 10. Are you distinguishing between "exercises" and "results"? I would say that there are only four results!

And what do you mean by "deriving an exercise by commutative law"? You can apply that to any sum.

I would answer the questions by either making or imagining an addition table (4 by 4 table) and counting directly or indirectly. Any way of counting can be considered combinatoric!
 
clarification

The problem needs a lot of clarification.
combinatoric!
There is a set {0, 1, 2, 3}.
The operation is addition.
The operation is operate only of two elements from the set.

If the result of the operation is 3 the result is internal result, because 3 is belong to the set. 2+1=3: {2, 1, 3} in {0, 1, 2, 3}
If the result is 5. 2+3=5. 5 is not in the set {0, 1, 2, 3}.

(1*) The number of exercise in the first is 4.
(2*) The number of exercise in the second is 6.

How I calculate with an combinatorics expression:
[1:] the (1*)
[2:] the (2*)
[3;] the number of exercises that obey 2+3=3+2 (commutative law) in (1*) ,...
[4;] the commutative law in (2*)
]5;] the commutative law in (1)+(2)?
 
Last edited:
There is a set {0, 1, 2, 3}.
The operation is addition.
The operation is operate only of two elements from the set.

If the result of the operation is 3 the result is internal result, because 3 is belong to the set. 2+1=3: {2, 1, 3} in {0, 1, 2, 3}
If the result is 5. 2+3=5. 5 is not in the set {0, 1, 2, 3}.

(1*) The number of exercise in the first is 4.
(2*) The number of exercise in the second is 6.

How I calculate with an combinatorics expression:
[1:] the (1*)
[2:] the (2*)
[3;] the number of exercises that obey 2+3=3+2 (commutative law) in (1*) ,...
[4;] the commutative law in (2*)
]5;] the commutative law in (1)+(2)?

You haven't answered my questions. What you restated is what I did understand.

I have no idea what you mean by "The number of exercise in the first is 4." What is an "exercise", as you understand it? And what, to you, counts as a "combinatoric expression"? Not all solutions of combinatoric problems use combinations or permutations, for example. I suppose you may just mean showing a calculation rather than a count; but there are several ways to do that.

Every expression "obeys" the commutative law; that is why it is called a law. Every expression you can form is still true when reversed, so that both would be in your list.

It will help if you show your own thinking, not using "combinatorics expressions", but just showing how you got the numbers 4 and 6, perhaps by listing the "exercises" they refer to. Examples often communicate more clearly than words, especially when there are language difficulties.
 
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