If the number of elements in a set is a nonnegative integer,we say that the set is_______

Q: Which sets are compact? The set of natural numbers less than some number M

A: We know that a set is compact if and only if it is closed and bounded. The set of natural numbers…

Q: Let A, B and C be sets. Use an element argument to prove the following. (A - B) n (B-A) = 0.

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Q: Using Pigeonhole principle to prove, if there exists 6 integers (between 1 and 10) in set S, then…

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Q: Suppose that A is the set of digits that construct your JUC ID, and B the set of even numbers less…

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Q: True or False If A is a set, the complement of A is the setof all the elements in the universal set…

A: Complement of a set A: Consider a set A. Then the complement of the set A is the set of all elements…

Q: 4. (10 points) Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite…

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Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: true or flase? Every infinite set is unbounded.

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Q: d. What is the cardinality of a countably infinite set?

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: 6. Suppose that U is an infinite universal set, and A and B are infinite subsets of U. Answer the…

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Q: 6. Identify whether the following are finite or infinite sets. a. The sets of first 50 natural…

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Q: The order of elements written in set builder notation matters. * O Always True O Never True O…

A: Given, The order of elements written in set builder notation matters,  We have to find the…

Q: Let the Universal Set, S, have 113 elements. A and B are subsets of S. Set A contains 77 elements…

A: From the provided information, n(U) = 113, n(A) = 77, n(B) = 17 And n (A Ո B) = 13

Q: Suppose A, B and C are finite sets of integers. Decide whether each of the following is a set, a…

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Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: If A is a countable set and B is a subset of A then BxA is an uncountable set BxA is not necessary a…

A: Given: A is countable and B is a subset of A so B also is countable.

Q: Which of the following sets is a universal set for the other four sets? O The set of even natural…

A: .

Q: (iii) ((A – B)UC – D) specified using set builder notation without any word -

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Q: 10. Let A be a proper subset of N (set of all natural numbers). Then, A cannot be equinumerous with…

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Q: If A is a subset of the set real numbers then A is a Borel set.

A: If A is a subset of the set of real numbers then A is a Borel set (True or False).

Q: Is {1, 3, 5} a subset of the set of odd integers?

A: {1, 3, 5}

Q: each of these pairs of sets in 1–3 determine whether the first is a subset of the second, the second…

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Q: If A is a countable set and B is a subset of A then BxA is a countable set BxA is an uncountable set…

A: We have to solve given problem:

Q: 1. For each of these pairs of sets, determine whether the first is a subset of the second, the…

A: A set A is said to be a subset of another set B if all the elements of set A are also contained in…

Q: 36. Let the universal set U = {r | x is a non-negative integer}. Let A = {x E U | x is divisible by…

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Q: For each of these pairs of sets in 1–3 determine whether the first is a subset of the second, the…

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Q: Show that the set of Natural Numbers (N) is a closed set.

A: The objective is to prove that the set of natural numbers is closed. To prove that it is closed we…

Q: 15. We have seen that an infinite set can be put into a one-to-one correspondence with a proper…

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Q: If A is a countable set and B is a subset of A then O None of these AxB is not necessary a countable…

A: If A is a countable set and B is a subset of A then

Q: The set of odd integers between 18 and 29 (inclusive) is: Write the set with the roster notation.

A: The objective of the question is rewrite the given sets in roster notation.

Q: 6. Find the complement of the following sets if universal set is the set of natural numbers. (a) {x…

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Q: Question 3 Use a Venn diagram to determine which relationship, ≤, =, or 2, is true for the pair of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Which of the following is an empty set? O set of cars with 10 doors OA-(tiger, lion, puma, cheetah,…

A: We have to find empty set from given options.

Q: 37. Let the universal set U = {x | x is a non-negative integer}. Let A = {x EU | x is divisible by…

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Q: Find the indicated number of elements by referring to Freshman Sophomores the table of enrollments…

A: From the, given information, it is observed that A the set of students from the college of arts…

Q: 3. Assume there is binary operation o that is defined for a set T which consist of two elements.…

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Q: Given a universal set containing integers from 0 to 21. Set A contains odd numbers while set B…

A: Let U denote the universal set. Then, U={0,1,2,..., 21} Union of two sets A and B  is a set…

Q: Remark. Every (finite Countable set is negligible or infinite)

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Q: Let the Universal Set, S, have 190 elements. A and B are subsets of S. Set A contains 95 element and…

A: Given Information: Universal set S has 190 elements. Set A contains 95 elements. Set B contains 78…

Q: 11. Use set-builder notation to represent X, the set of all whole numbers greater than 20. X-(x/x is…

A: The set builder notation of the set of all whole numbers greater than 20 is,

Q: 2. Write the set of positive odd integers in set-builder notation.

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Q: Show that if A is a countable set, and B CA is infinite, then B is countable. [Hint: How could we…

A: To prove that  If A is a countable set and B is a subset or equals to A is infinite then B is…

Q: 5. Use element proof to show that for any sets A and B, if A ≤ B then A U B = B. 6. Construct an…

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Q: 6. Identify whether the following are finite or infinite sets. a. The sets of first 50 natural…

A: To Identify the finite and infinite sets.

Q: What is the cardinality of the set of integers X defined below? X={n| 1<n<12 n is not divisible by…

A: Introduction :

Q: Which of the following is the correct representation of A = (2,4.8.16.32. in set builder notation? A…

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Q: In the Venn diagram, the universal set, S, represents all positive integers less than 10. O 2020…

A: if A is a universal set and B is any subset of A then complement of B denoted as  Bc is defined as…

Q: 4. Suppose you wanted ; –) and :0 to be the elements of a set S. (a) How could you indicate this? In…

A: We want ;-) and :o to be the elements of a set S.