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

Q: 5. Suppose that A is a set and {Bn}nɛI is an indexed family of sets. Prove that A - UB, = N(A – B„).…

A: I have given the proof using the properties of sets

Q: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

A:

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let A…

Q: 1) Define a subset.

A: To define a subset.

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

A:

Q: Given a universal set U for a set X , if AC X , then (U – X) n A = Ø

A: Given a universal set U for a set X and A⊆X We shall prove it by contradiction method. Let us assume…

Q: Prove that if A is transitive set, then A+ is also a transitive set.

A:

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: Give an Such that. example of sets A andB

A: Universal Set: We consider all the sets to be the subsets of a given set known as the universal set…

Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

A:

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

Q: If sets X and Y are countable, then prove or disprove that X-Y is uncountable.

A:

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: A set is not open if its complement is not closed. O True O False

A: To find the given statement is true or false .

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: Suppose that X and Y are sets such that the power set of Y is a subset of the power set of X. Does…

A:

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 150, n(B) = 90, and n(A ∩…

A:

Q: The empty set o is open set ylgn O İhi O

A: See the detailed solution below.

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

A:

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: Draw a ven diagram for this set (A ∩ B) ∪ (A ∩ C')

A:

Q: Prove that if A is a set then so is {A}!

A:

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not ?

A:

Q: IF A IS A +IELD 1HEN THE SET AnB BELONGS in A.

A: According to question We have to choose the the given statement is true or false.

Q: If A, B, and C are sets such that A ∩ B ≠ Ø and B ∩ C ≠ Ø, then A ∩ C ≠ Ø

A:

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly

A: Set equality

Q: If A, B and C are sets such that; A ∆ B = A ∆ C, then   B is a subset of C        Select one: A.…

A: The meaning of A ∆ B is A ∆ B = (A u B) - (A n B) So A ∆ B contains that elements from set A and set…

Q: The empty set is open set ylgn O İhi O

A: The complement of an empty set is the whole set, which of course contains everything including all…

Q: It is the selection of objects from a set.

A: This is the problem of combinatorial. finite math, counting.

Q: Let A be a well-ordered set, then every subset of A is not well-ordered

A:

Q: If A and B are sets containing finitely many elements, then |A x B| =|B x A|.

A:

Q: prove that the union of a countable set and an uncountable set is uncountable

A:

Q: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

A: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

Q: 4. Prove that the set Z is a closed set in R.

A:

Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

A: Given that set A and set B have 6 and 9 respectively. Now that A is a proper subset of B which means…

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

Q: a. How many subsets are there of the set {0, 1, 2, 3, .., 10}? b. How many maps of this set into…

A:

Q: If A is an uncountable set and A is a subset of B then O None of these BxB is not necessary an…

A: Countable Set: A set A is called countable if it is either finite or countably infinite. In case of…

Q: Show that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

A:

Q: Determine whether each of the following statements is true or false, and explain why.A set is a…

A: A set A is subset of another set B if all elements of the set A are elements of the set B.

Q: Give an example of a set A such that there is a set B with B as the element of A but B is a subset…

A: Give an example of a set A such that there is a set B with B as the element of A but B is a subset…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.