Can AUB can be said as a relation or not between A and B sets?

In summary, the conversation discusses whether AUB can be considered a relation between two sets A and B. The speaker argues that AUB, as a string of symbols, does not have any inherent meaning and that the connection between two sets should be specified where "AUB" is written. They also mention that AUB may not be the appropriate way to denote a relation between two sets.
  • #1
Huygen121
7
0
My question is just to ask whether the operations like:-

AUB is a relation or not?

in our book it is written that the relations of two sets should be subset of the cartesian product of two sets but i think that relations are those which connects two sets and that can be AUB(A union B) also,because it connects two sets either.

so,i want to ask whether AUB can be said as a relation or not between A and B sets
 
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  • #2
"AUB" is a string of three symbols without any meaning, unless A, U and B get specified. That should be done where "AUB" is written, not at some random position afterwards.

because it connects two sets either.
That is not the sort of connection you need.
so,i want to ask whether AUB can be said as a relation or not between A and B sets
No.
 

1. What is a relation in the context of sets A and B?

A relation between two sets A and B is a connection or association between elements of the two sets. It is a way of describing how elements in one set are related to elements in the other set.

2. How can a relation be determined between sets A and B?

A relation between sets A and B can be determined by examining the elements in both sets and identifying any patterns or connections between them. This can be done by looking at the elements themselves, or by using set operations such as intersection, union, or complement.

3. Can all sets A and B have a relation?

Yes, all sets A and B can have a relation. The relation may be trivial (i.e. all elements in A are related to all elements in B), but there will still be a relation between the two sets.

4. What is the relevance of AUB in determining a relation between A and B sets?

The union of sets A and B, denoted by AUB, refers to the set of all elements that are in either A or B (or both). This can be useful in determining a relation between A and B, as it allows for a comparison of all elements in both sets.

5. Can AUB be used to prove or disprove a relation between A and B sets?

Yes, AUB can be used to prove or disprove a relation between A and B sets. If the union of A and B contains all elements from both sets, it indicates a strong relation between the two sets. On the other hand, if the union does not contain all elements from both sets, it may suggest a weaker or non-existent relation between them.

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