Let U= (1,2,3, ...,20}. Write the following sets by listing the elements in braces. (a) {xEU|x is even and 10

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Given information- We have given that the set S has 7 elements. We have to find the number of subset…

Q: Let's compare the cardinalities of N and I.

A: We will find out the required solution.

Q: Suppose S is a set with cardinality n. What is the cardinality of the power set of S ? Are there any…

A: Suppose S is a set with cardinality n. Then power set of S contains 2n elements . Power set of any…

Q: 2. a. List all 3-combinations for the set {x1, x2, x3, X4, Xs}. Deduce the value of (,). b. List all…

A:

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: 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: If lal = n, show that |a'| %3D gcd(n,t)

A:

Q: A large corporation classifies its many divisions by their performance in the preceding year. Let P…

A:

Q: TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B =…

A:

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

A:

Q: 5. Give an example (by words) for a collection of objects which is not well defined

A: Given, We have to write an example for a collection of objects which is not well defined.

Q: Suppose (S;)jEN is a sequence of subsets of R", such that each S; C R" has ieN zero content (i.e.,…

A: Option 1, 3, 4,5,6 are true.

Q: If 3 -letter words" are formed using the letters A, B, C, D, E, F, G, how many such %3D words are…

A:

Q: Suppose that A and B are sets. A is a subset of X and B is also a subset of X. Please teach me how…

A:

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: We have to solve given problem:

Q: 2. (i) Show that given finitely many countable sets A1, A2, , An, the set A1 x A2 x .. x An is also…

A:

Q: 10. Two sets are called disjoint if they have no elements in common, i.e., if their intersection is…

A: Note that two sets are called disjoint if they have no elements in common, that is, if their…

Q: А - (ВnС) %3D(А — В) n (А — С)

A:

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: SUppose K,n EZ and O < Kcn. Prove +hat by (onsi nsi dering subsets of (1,... --- --- (^) - (":') + (…

A: The given problem is to prove the following identity using the basic mathematical identities.

Q: 4) Using equality of sets, prove that (An B)' = A' U B'

A: we know thatA∪B=x: x∈A or x∈BA∩B=x: x∈A or x∈BA'=x:x∈U, x∉A=U \ AWhere U is a universal set.That is…

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 X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

A:

Q: (4.2) Let X = {1,2, 3, 4} and 7 = {0, {1,2,3} , {2, 3},{1},X} be the topology defined on X. (a) Show…

A:

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

A:

Q: 2) het A, B and non- dijoint diagranı be Three Cveyla Ony using sets von Show (B-C)Ule- A) # A-8

A: firstly, we will draw all given set region then we comparing both side

Q: Let Σ be a set of well formed formulas and α, β be well formed formulas. Show thatΣ ∪ {α} |= β if…

A: If Σ⊨(α→β), and (Σ∪{α}) holds, then both Σ and α hold (a set is only true if every member of the set…

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

A:

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

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: Let E be the set of 26 English letters. Find the number of 5-letter words (including  nonsensical…

A: There are totally 26 English letters in which 5 are vowels(A, E, I, O, U) and remaining 21 are…

Q: What is the best choice for the cardinality of A X B when A is finite and not empty, and B is…

A: Given:A=Finite and non emptyB=uncountableCardinality:A×B=Product of A is finite and and B is…

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: 2. If the set S in each part is finite, write down S. i. S={primes) ii. S= (even primes) iii. S=…

A: 2. Given that S in each part is finite . i. S={Primes}. S={2,3,5...}. This set has infinitely many…

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

A: When two sets A and B overlap that is A = B, then the intersection and union of the  sets A and B…

Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

A:

Q: Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: A ∩ B ̸ =…

A: We have to give an example of 4 non-empty sets A, B, C, D such that all the following are…

Q: 6. Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below…

A: (i). Let  S = { ..., -5, - 4, - 3, - 2, - 1 }

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: .4.12 (a) Show that if X and Y are countable sets, then their union XUY Countable. (b) Prove that…

A: We prove following theorem by contradiction

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: 6. Determine all the possible topologies X = {1, 2, 3, 4, 5, a, b, c² 3 sex

A:

Q: A set X with one element has topologies. * O Two One O Infinite Zero O O O O

A: Let X={a}. Then P(X)=T={Ø , X} is the only topology on X.

Q: 8. Given the set B={2,3,4} such that (a,b) are the two numbers having the same parity therefore R2…

A:

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

A:

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: 5. Consider the generic Venn diagram for three sets. (a) Add one figure showing a fourth set D. (b)…

A: The generic Venn diagram is:

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”.