If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A equals: N(A)+ N(A,) + + N(A,) O True O False

Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: How many proper subsets does the set W, containing the days of the week, have? W={Monday, Tuesday,…

A:

Q: Let the Universal Set, S, have 92 elements. A and B are subsets of S. Set A contains 12 elements and…

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: (2) (a) Give an element chasing proof to show that the empty set Ø is a subset of any set A. (b)…

A:

Q: Suppose that S is a non-empty finite set. Prove that ? has as many even-sized subsets as it does…

A: Let S be a non-empty set. Let A be the set of even sized subsets of S and let B be the set of odd…

Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

A:

Q: 1) Define a subset.

A: To define a subset.

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

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: 2. Show that any subset of a countable set is countable. 3. Show that a nonempty set S is countable…

A: Hence any subset of a countable set is countable.

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: Let U be universal set of all the students of Class X of a coeducational school and A be the set of…

A: In a coeducational school, there can be only boys and girls in school. Since, A is the set of all…

Q: Elements that are in the universal set but not in the set A, are members of the set called, of A.…

A: Universal set : Any set that contains all the sets is called Universal set Subset:  All the elements…

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where B =…

A:

Q: A universal​ set, with​ n(U) = 30​, is partitioned into three​ subsets: A,​ B, and C.     If​ n(B) =…

A: we are given n(U) =30​, n(B) =3​⋅n(A), and​ n(C) =2​⋅n(B) also universal set is partitioned into…

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: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

Q: 8. (a) Show that the intersection of finitely many open sets is open.

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

Q: 1. Let X-(a,b,c} and T X={Ø,X,{a},{b},{a,B}}, (i) Write down all open subsets of X. (ii) Write down…

A: If (X,T_X) is a topological space. Then elements of T_X is called open sets and a set is closed if…

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

A:

Q: Prove that A is an infinite set if and only if ∀n ∈ ω, A has a subset B such that B ≈ n.

A: given that A is an infinite set let B be any set let prove this contradiction suppose assume that B…

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: 10. The supremum of a non-empty set S, if it exists, is always unique.

A: We need to prove that Supremum of a non empty set S, if it exists, is always unique.

Q: Prove that every infinite set S contains a proper subset similar to S.

A: We have to prove that every infinite set S contains a proper subset similar to S. Let X=S Let X be…

Q: 5.3.8 Prove that if A CR is a finite set, then A is well-ordered.

A:

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

A:

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

A: Set equality

Q: 2. Specify the set B in set-builder form by giving a written description of its elements, where…

A:

Q: Determine the number of distinct proper subsets for the given set {c, a, v, e}.

A:

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

A:

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: a)​ n(A ∪ ​B) ​b) nA′ ∪ C ​c)

A:

Q: (a) The intersection of an arbitrary collection of closed sets is closed. (b) The union of any…

A: (a) We have to prove that the intersection of an arbitrary collection of closed sets is closed. Let…

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

A:

Q: 3. Let X be a set. Call a subset A C X to be finitely complemental if its complement is either…

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

A:

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

A:

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: Let A1,A2,.......,An be countable sets. Prove that  A1 x A2 x.............An = { a1, a2,…

A: Let A1,A2,.......,An be countable sets. Then we have to show that    A1 x A2 x.............An = {…

Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and S, the…

A: The set A=t,u,v,wS1 be the set of all subsets of A that do not contain wS2 be the set of all subsets…

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

A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

Q: (4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all…

A:

Q: Let U = {6, 7, 8, 9, 10, 11, 12}, and A = {6, 7, 8, 9}. List all the members of the given set.  Ā

A: The Universal set U is defined as U = {6, 7, 8, 9, 10, 11, 12}.

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.