Proving Set Theory Union in Cartesian Products

In summary, set theory union is an operation that combines two sets into one set, using the symbol ∪ (pronounced "cup") to indicate the union operation. It differs from set theory intersection in that it combines elements from both sets, while intersection only includes common elements. The set theory union operation can be applied to any number of sets and has various real-life applications, such as in mathematics, computer science, and statistics.
  • #1
rallycar18
9
0

Homework Statement



Suppose A,B,C are sets. Prove that

A× (B U C)= (AxB) U (C x A)
 
Last edited:
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  • #2
Have you tried the usual inclusion both ways method?
 
  • #3
VeeEight said:
Have you tried the usual inclusion both ways method?

I'm not familiar..
 
  • #4
Well if A is contained in B and B is contained in A, then A=B.
 
  • #5
assume [itex] x \in A \times (B \cup C) [/itex]. Think about the definitions of Cartesian product and union: what can you conclude about the element [itex] x [/itex]; can you use this information to show [itex] x \in (A \times B) \cup (A \times C) [/itex]?
 

Related to Proving Set Theory Union in Cartesian Products

1. What is the definition of set theory union?

Set theory union is an operation that combines two sets into one set, where the resulting set contains all the elements from both sets without any duplicates.

2. How is set theory union symbolically represented?

The symbol for set theory union is ∪ (pronounced "cup"). It is placed between two sets to indicate the union operation.

3. What is the difference between set theory union and intersection?

The main difference between set theory union and intersection is that union combines elements from both sets, while intersection only includes elements that are common to both sets.

4. Can the set theory union operation be applied to more than two sets?

Yes, the set theory union operation can be applied to any number of sets. The resulting set will contain all the elements from all the sets without any duplicates.

5. How is set theory union used in real life?

Set theory union has many applications in fields such as mathematics, computer science, and statistics. It can be used to combine data from multiple sources, find commonalities among different groups, and solve problems related to overlapping sets.

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