Question
Asked May 8, 2019

Let F be a nontrivial on X. Prove that the follow-

ing statements are equivalent
1. F is an ultrafilter.
2. (∀A⊆X)A∈F ↔ X−A∈/F.
3. (∀A,B⊆X)A∪B∈F → A∈F or B∈F.

check_circleExpert Solution
Step 1

Let F be a non trivial on X.

To prove that the statements are equivalent:

fullscreen
Step 2

Proof:

Assume (1) is true.

Assume there is a set A that is a subset of X.

Then by definition of ultrafilter, for any

fullscreen
Step 3

When A belongs to F, then X – A does not belong to F but be...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: I do not understand how to do number 6 and 7. Can you explain me? Thank you.

A: The sets are given as B, O, N, U, S.In order to find the number of two-way intersections like (N∩B, ...

question_answer

Q: z is a complex variable, z=x+iy determine which of the following functions u are harmonic. For each ...

A: To check if the function u is harmonic, and in that case , find its harmonic conjugate v

question_answer

Q: Parallel circuit:e=12 voltsR1=4 ohmsR2=4 ohmsIt= ?

A: The circuit diagram can be drawn as given below.

question_answer

Q: Subject: Elements of Set Theory Greetings,I am really having difficult time with these problems that...

A: (a)We have to prove:

question_answer

Q: 5.1 Calculate the following operations of intervals b) [5,91 [5, 10] c) [6,10] )-1, 5] d) 13,71[-3,-...

A: Compute the sum of two intervals.

question_answer

Q: Problem B. Recall that a order relation is a well-ordering, if every nonempty set has a smallest ele...

A: Click to see the answer

question_answer

Q: the book is "First Course on Fuzzy Theory and Applications"

A: The formula to compute the membership fuctions is as follows.

question_answer

Q: Q- Let S be a set on which an associative binary operation · has been defined such that S contains a...

A: To verify that U(S) satisfies the axioms of a group (under the given conditions)

question_answer

Q: Solve the linear system by the Gauss Jordan Elimination Method: 4x - 4y + 4z = -8 x - 2y - 2z = -1 2...

A: To bring (reduce) the given system of equations to triangular form and then to diagonal form  and th...