DeMorgan's Laws: Infinite Unions & Intersections

[ehrenfest]

Homework Statement

Do deMorgan's laws hold for infinite unions and intersections i.e.

is $$X-\cap_{i=1}^{\infty}U_i = \cup_{i=1}^{\infty}(X-U_i)$$

?

Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

I'm fairly certain the proof is exactly the same as it would be for a finite number