Question

Show(prove) that the intersection of two compact sets is
compact.

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Answer #1

Prove the following:
The intersection of two open sets is compact if and only if it
is empty. Can the intersection of an infinite collection of open
sets be a non-empty compact set?

Prove that the union of two compact sets is compact using the
fact that every open cover has a finite subcover.

Prove the following for the plane.
a.) The intersection of two closed sets is closed.
b.) The intersection of two open sets is open.

Prove whether or not the intersection and union of two
uncountable sets must be uncountable

Show (prove), from the original definition of the integers, that
subtraction of
integers is well defined.
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Show (prove) that the set of polynomials of degree less than or
equal to 7 with
real coefficients should be uncountable.
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Show (prove) that the set of sequences of 0s and 1s with only
finitely many
nonzero terms should be countable.
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Q: Provide three distinct examples of groups of order 8.
I will give a thumbs up. Thank you. Please try to use group Z if
possible.

Show that the symmetric difference of two sets is equal to the
union of the two sets minus the intersection of the two sets:
(A\B)U(B\A)=(AUB)\(A intersect B).

Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is the set containing the elements that are in both
A and B. That is, A ∩ B =
{x : x ∈ A and x ∈
B}.
Two sets A and B are
disjoint if they have no elements in common. That
is, if A ∩ B = ∅.
Given two sets A and B, the union of
these sets, denoted A ∪ B,...

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