Steps To prove that: An (Uier Bi) = Uier (An Bi) we need to show that both sides of the equation are equal. This involves proving two inclusions: An (Uier Bi) ≤ UiÊI (AN Bi)and Ur (An Bi) ≤ An (Uie Bi) Ui Є I Proof: Part 1: An (UIB₁) C Uiel (An Bi) Let x E An (Uier Bi). By the definition of intersection and union, this means that: Let A be a set, and let {B}ier be an indexed family of sets. Prove that An (UB.) - U (An B.). iЄl JL
Steps To prove that: An (Uier Bi) = Uier (An Bi) we need to show that both sides of the equation are equal. This involves proving two inclusions: An (Uier Bi) ≤ UiÊI (AN Bi)and Ur (An Bi) ≤ An (Uie Bi) Ui Є I Proof: Part 1: An (UIB₁) C Uiel (An Bi) Let x E An (Uier Bi). By the definition of intersection and union, this means that: Let A be a set, and let {B}ier be an indexed family of sets. Prove that An (UB.) - U (An B.). iЄl JL
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I don't understand why you put Ui element of I. I think you made a mistake. Please let me know. Thank you.
Transcribed Image Text:Steps
To prove that:
An (Uier Bi) = Uier (An
Bi)
we need to show that both sides of
the equation are equal. This involves
proving two inclusions:
An (Uier Bi) ≤ UiÊI (AN
Bi)and Ur (An Bi) ≤ An
(Uie Bi) Ui Є I
Proof:
Part 1: An (UIB₁) C
Uiel (An Bi)
Let x E An (Uier Bi). By the
definition of intersection and union,
this means that:
Transcribed Image Text:Let A be a set, and let {B}ier be an indexed family of sets. Prove that
An (UB.) - U (An B.).
iЄl
JL
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