Proof about operations on sets

[chocolatelover]

Homework Statement

Let the set Ar: r is an element of all real numbers and the set Br: r is an element of all real numbers be two indexed families of sets.

Prove that (upside U r is an element of the reals Ar) U (upside U r is an element of the reals Br) is a subset of upside U r is an element of the reals (ArUBr).

Homework Equations

The Attempt at a Solution

Could someone please give me a hint? I know that Ar and Br have to be unions of each other and at the same they are subsets of the other one, but I don't really know how I would go about proving this.

Thank you much

 

[Dick]

That's kind of hard to read. But if x is an element of the left hand side, then it's either in all of the A_r or it's in all of the B_r. If x is in the right hand side then it's in either A_r or B_r for all r. Assume each of the conditions on the left and prove they imply the right.

 

[chocolatelover]

Thank you very much

Regards