Symmetric set

[Nickfytas]

Suppose we have a bounded and connected subset D of R^2 and it is symmetric with respect to the x-axis
Is it true that D1=D2 and why.
Where D1={(x,y)eD : y>=0} and D2={(x,y)eD : y<0}

 

[HallsofIvy]

I would not say "D1= D2". We reserve "=" to mean they are the same thing which is not the case. it is true that D1 and D2 have the same area, the same "shape", etc..

 

[Deleted member 4993]

Suppose we have a bounded and connected subset D of R^2 and it is symmetric with respect to the x-axis
Is it true that D1=D2 and why.
Where D1={(x,y)eD : y>=0} and D2={(x,y)eD : y<0}

What/which methods were you taught to investigate symmetry?

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Nickfytas]

I would not say "D1= D2". We reserve "=" to mean they are the same thing which is not the case. it is true that D1 and D2 have the same area, the same "shape", etc..

I want to prove that the integral in D is 2 times the integral in the D1 and I can’t it prove without saying D1=D2

 

[HallsofIvy]

No, you want to say that the integral in D1 and the integral in D2 are the same number, NOT that D1 and D2 are the same set!

 

[Deleted member 4993]

I want to prove that the integral in D is 2 times the integral in the D1 and I can’t it prove without saying D1=D2

You need to show your work - so that we know where to begin to help you.

You have not shown any work - you have just stated what you don't want to do.

What does symmetry in sets mean to you?

 

[Nickfytas]

I see .
So far I have done this . But I want to prove it using integral algebra not just words