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ehrenfest
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Homework Statement
Do deMorgan's laws hold for infinite unions and intersections i.e.
is [tex]X-\cap_{i=1}^{\infty}U_i = \cup_{i=1}^{\infty}(X-U_i)[/tex]
?
Homework Equations
The Attempt at a Solution
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DeMorgan's Laws are a set of rules in mathematics and logic that describe the relationship between unions and intersections of sets. They state that the complement of the union of two sets is equal to the intersection of their complements, and vice versa.
DeMorgan's Laws are used to simplify and manipulate logical expressions, particularly in Boolean algebra. They can also be applied in set theory to determine the relationship between different sets.
An infinite union is a union of an infinite number of sets. This means that the union contains all the elements that are present in at least one of the sets, even if there are an infinite number of sets.
An infinite intersection is an intersection of an infinite number of sets. This means that the intersection contains only the elements that are present in all of the sets, even if there are an infinite number of sets.
DeMorgan's Laws can be applied to infinite unions and intersections in the same way as they are applied to finite unions and intersections. The complement of an infinite union is equal to the intersection of the complements of the individual sets, and vice versa.