Calculating Strange Union

by xx01   Last Updated August 01, 2020 11:20 AM - source

Hello everyone assume that we set $A$ = {{1 ,2} , {2 ,3} ,{4 ,3}}

so what is $\cup_{B \in A} (B)$?

Answers 3

$\{1,2\}\cup \{2,3\} \cup \{4,3\}$..

August 01, 2020 10:51 AM

Here The elements of $A$ are $\{1,2\}, \{2,3\}, \{4,3\}$. So the union of elements of $A$ is:

$$\cup_{B\in A} B = \{1,2\} \cup \{2,3\} \cup \{4,3\}.$$

August 01, 2020 10:56 AM

I surmise that this was a trick question. The intention is for the student to realize that the union of all elements of a specific set is the specific set itself, without any regard to what the elements actually are.


Subsequent comments by Aurelio and Coward have suggested that I am mistaken. I may well be mistaken, but I'm just not seeing it yet.

Coward: In response to your comment, could you please provide a counter example?

Aurelio: In response to your counter example, perhaps I'm missing something here. In your counter example, it does seem to me that $\bigcup_{b \in A} \;=\; A.$ Please explain if you think that I am mistaken.

August 01, 2020 10:58 AM

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