Is it possible for two nonempty sets to have the same intersec-tion and union? If so, give an example.

Q: If  X is a countable set show that every topology on X is second countable.

A: To Show: If  X is a countable set show that every topology on X is second countable.

Q: Let S be a set with |S|=6 . In how many ways can we partition the set S into three non-empty parts?

A: Answer:   3   Here    |S| = 6 So there are total 11 possible partitions which are 6 5+1 4+2 3+3…

Q: 4. Give an example of a non-measurable subset of R. (witheutProof)

A:

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

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: 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: Let A be the set of even positive integers less than 40 and divisible by 4. What is the cardinality?

A: This is the question from set theory.

Q: Let A = {distinct letters occurring in the word HIPPOPOTAMUS}. What is |A|, the cardinality of the…

A: Cardinality of a set is defined as the number of distinct element in that set.

Q: 4. Let S be any nonempty set with the operation a * b = a. Is (S,*) a semigroup? Is it commutative?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: SA

A: We will understand about the SAS and Donkey Theorem.  SAS :- SIDE-ANGLE-SIDE (SAS) theorem: If two…

Q: How many subsets of S do not contain any upper case letters?

A: given set S=A,B,a,b,c,d,1,2,3,4 claim- to find how many subsets of Sdo not contain any upper case…

Q: Show that every open set with respect to 7 is a union of open ball(s).

A:

Q: А - (ВnС) %3D(А — В) n (А — С)

A:

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: What is meant by the Cardinality of a finite set? Give one example.

A: The cardinality of a set is meant by the number of elements of the given set. If the set has no…

Q: Consider the set C={Ø,{Ø},{Ø,{Ø}}}. How many elements are there in the power set P(C)? *

A:

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: Show that the countable collection B = {(a,b) × (c, d)| a <b and c< d,

A:

Q: Does the set S = span M22?

A: The given set is S=1100, 0011, 1001, 0111. Note that the above set is linearly independent set.

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: How can the union and intersection of n sets that all are subsets of the universal set U be found…

A:

Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

Q: subset

A:

Q: union of a collectionm of connected sets that have a point in common is conne

A:

Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

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

A:

Q: If the union of two sets is countable, then each set is also countable.

A:

Q: Calculate the number of subsets and proper subsets for the following set: {x |x is single-digit…

A:

Q: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: {0,1,3,4,5} is the smallest set that contains {1, 3, 4} and {0, 3, 5} as sub-sets.

Q: Prove that every nonempty subset of a well-ordered set is well-ordered.

A: Given problem is :

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: Prove that Everry subset of negigible seti's gigible

A:

Q: Is the set (9, 20] under usual order ≤ well-ordered? Why?

A: We need to determine the set (9 , 20] under usual order is well - ordered or not. We know that , a…

Q: The closare of a set is smallest closed set containing s صواب ihi

A: Let S be a subset of X: S⊆X. Let M be the closure of S. Then M is the smallest closed set which…

Q: open

A:

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are…

A: Given that X=a,b,c. To construct two topologies that have at least four open sets. We know that in…

Q: ind the all possible number of different multi sets of size '4' from -element set, in which at least…

A: In this question, the concept of permutation is applied. Permutation Permutations are frequently…

Q: A set has 9 elements. How many subsets of S are there with at most 2 elements?

A: Given,            A set has 9 elements. Subsets of S are there with at most 2 elements.

Q: If set K is such that n(K) = 3, then set K has 6 subsets

A:

Q: Mathematical Definition: What is a linerarly independent set S?

A: Let S be a non empty set. S = { v1, v2, v3 .... vn}

Q: Draw a diagram out of these sets

A:

Q: Define subsets and give a relevant example along with it.

A:

Q: is the cardinality of the set {characters in set A}?

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: (P,<) is a nonempty partially ordered set such that every chain in P has an upper bound, then P has…

A:

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”.