Which of the following statement is not true? * Disjoint set is a set which contains all objects. Complement is the set of all elements in the given universal set that are not in the given set. Intersection of sets contains the elements that two sets have in common. Union of sets refers to the set of elements that both two or more sets have

Q: Let the Universal Set, S, have 146 elements. A and B are subsets of S. Set A contains 84 elements…

A: Given that universal Set  S have 146 elements. Set A contains 84 elements. Set B contains 25…

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | x is a…

A: In roster notation, all the elements of a set are listed. In this notation each element is separated…

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: Why eat subset in your list and roster form if there is more than one subset in your list separate…

A: use the set property.

Q: i. Provide an example to prove that the arbitrary intersection of open sets is not an open set ii.…

A:

Q: Give an example to show arbitrary union of open sets is again open. Is the result true for arbitrary…

A:

Q: Specify the set B in set-builder form by giving a written description of its elements, where…

A: given B={0,1,4,9,16,25} B=0,12,22,32,42,52

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: Determine whether the set spans all of M2. Justify your answer with your work and/or written…

A:

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…

A:

Q: 11. For all sets A, B, and C, A N (B- C) C (AN B)– (A N C). |

A:

Q: Can sets have different names? Give a precise definition of a set. Give two different notations…

A: A set can be defined in mathematical terms or not in mathematical terms. A way of representing sets…

Q: | If two sets are equivalent, then they are also equal. (True or False?) A is not a subset of B.…

A: These are discussed according to definition in set theory.

Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

A:

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: The set subtraction law states that A – B = ANB. Use the set subtraction law as well as the other…

A: The given statement: For any sets A and B, A∩B-A=∅.

Q: Prove the following statement. Assume that all sets are subsets of a universal set U. For all sets A…

A: Given For all sets A and B, if  Ac ⊆ B  We prove that A ∪ B = U.

Q: Use element argument to prove the statement. Assume that all sets are subsets of a universal set U,…

A: The given statement is 'for all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C).'

Q: 8. Give an example to show that the arbitrary intersection of open sets is not an open set. 9. Give…

A:

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Let U={x | x is a letter in the English alphabet} be the universal set. Consider the set B={c, m, n,…

A: Let U={x | x is a letter in the English alphabet} be the universal set. Consider the set B={c, m, n,…

Q: Determine if the union/intersection of two open sets is always open then determine if the…

A:

Q: Let the Universal Set, S, have 141 elements. A and B are subsets of S. Set A contains 96 elements…

A: Universal set S contains 141 elements. Set A contains 96 elements. Set B contains 57 elements. Total…

Q: two example of open set in R, closed set in R, and the closure of that set

A:

Q: 4. Explain how bijection can be used to define the cardinality of an infinite set. Using that idea,…

A:

Q: Suppose you have to use an element argument to prove the following statement. (Assume that all sets…

A:

Q: Denote the set in set-builder form {6, 12, 18, ….66}

A: The objective is to denote the set {6, 12, 18, ….66} in set-builder form.

Q: Use element argument method to prove that if A and B are sets such that P(A) ≤ P(B), then A ≤ B,…

A: I just used the definition  Of power set and subset of set

Q: Identify the set shown below as finite or infinite, {10, 11, 12, ..., 40} ..... OInfinite O Finite

A:

Q: Which of the following sets are closed under addition? Choose ALL that apply.

A: A set A is closed under addition, if for every x and y belong to A then x+y also belong to A.

Q: Please help me with this. Use element argument to prove the statement. Assume that all sets are…

A:

Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

A:

Q: Write an example of a partially ordered set which is not totally ordered. Explain the reasons. Are…

A:

Q: Prove directly that the union of two disjoint sets, where one is countably infinite and the other is…

A:

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: Prove that the greatest member of a set, if exits, is the least upper bound of the set,

A:

Q: Please prove the statement below: For all sets X, Y, and Z subsets of a universal set U (X -- Y) ∩…

A:

Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Let the Universal Set, S, have 101 elements. A and B are subsets of S. Set A contains 59 elements…

A: It is given that,  set A contain 59 elements, n(A) =59 Set B contain 38 elements, n(B) =38 Set A and…

Q: 4.3 Give an example to show that the arbitrary intersection of open sets is not an open set.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: The defining property of an ordered pair is that two or- dered pairs are equal if and only if their…

A: Firstly suppose that a,b=c,d i.e a,a,b=c,c,d. We have to show that a=c & b=d. There will be two…

Q: show vacuous proof of statement that "empty set is a subset of any set"

A:

Q: State whether each of the following statements is true or falm. Then give an explanation, proof or…

A: It is given that S and T be equivalence relation on set B.

Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: Give example for following 1/ set is not compact

A: Compact set:- A set S⊆R is called compact “if every sequence in S has a subsequence that converges…

Q: The union of the universal set and any of its subset is * none of the choices cannot be determined…

A: our objective is to conclude