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

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it…

A: We have a subset S of {1,2,.......,100} with |S| = 26. We have to prove that S contains at least one…

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

A:

Q: Let A be a set with |A| = n. Using induction, prove that |P(A)| = 2^n .

A: To show that the cardinality of power set of A is 2n when given that cardinality of A is n.

Q: Suppose X is a set with 84 elements that is partitioned into four subsets: X1, X2, X3, and X4. If X1…

A: Given total number of elements = 84 Let  number of elements in X4 be a As X1 has twice as many…

Q: Let N be the set of all integers (x = r) and ( the class of all subsets of N.

A: Consider, the Measurable space,

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: Prove that the set of all finite subsets of N is countable infinite.

A: We have to prove that the set of all finite subsets of N is countable infinite. Since,…

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: 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: 5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre- spondences…

A:

Q: How many sets of are in 2-½?

A:

Q: Suppose a set A is uncountably infinite, that U is countably infinite, and that UC A. Show that A -…

A:

Q: Cantor set is uncountable .A O

A:

Q: Example 2.3 Let A be a set with A = n <x. How many distinct subsets does A have?

A:

Q: Given H={ z∣ z ∈  N and 454< z< 475} Hhas   subsets. H has   proper subsets.

A: Given H={ z∣ z ∈  N and 454&lt; z&lt; 475}Hhas   subsets.H has   proper subsets

Q: 4,P) is a aɔnds (a) The intersection of any collection of closed sets in X is closed (in X). (b) The…

A:

Q: For each n ≥ 3, find the number of subsets of {1, 2, . . . , n} of cardinality greater than 2 with…

A: Let X=1,2,3,....n The number of subsets of X with m elements is given by, Cmn

Q: If any subset of size five is chosen from {1, -1, 2, -2, 4, -4, 8, -8), then prove that each of the…

A:

Q: about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of…

A: Let there are x elements in X2. So there are 6x elements in X1. There are 3x elements in X3. Given…

Q: 4. Let A be an open set in å nörmed space subset B of X .

A: Que  Ans :  Given ( X, ||-||) be a norm linear space,  A be any open subset of X    ( def- set A is…

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: 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: 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: 7. Give an example of an indexed collection {An nE N} such that 1 An and U An = Aj = N.

A: Given that An|n∈ℕ To give an example of an indexed collection  An|n∈ℕ such that ∩n=1∞An=∅ and…

Q: 6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤…

A: Please find the answer in next step

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

A:

Q: (a) Show that a set S in R" is convex if and only if for each integer k, every combination of any k…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we will…

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: Give an example of sets {An}n≥1 such that for each n ≥ 1, the set An ⊂ [0, 1] is both compact and…

A: Construct sets Ann≥1 such that for each n≥1, the set An⊂0, 1 is both compact and connected, but the…

Q: 15. We have seen that an infinite set can be put into a one-to-one correspondence with a proper…

A:

Q: Suppose A is a set for which |A| = 12. How many 5-element subsets of A are %3D there? (the number of…

A: Here given   A is set for which |A| = 12  So here no of elements in set A = 12

Q: Enumerate

A: The set S contains 5 elements, Number of subset = 25 = 32

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: 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: For every positive integer n, prove that a set with exactly n elementshas exactly 2n subsets…

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: 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: Suppose A1, A2,... is a sequence of subsets of R. Then U Ak < EIAKI. k31 k=1

A: The statement can be proved using method of induction.

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

Q: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…

Q: 2. Prove that the union of any finite collection of closed sets in RP is a closed set in RP.

A: A set A is closed if and only if every limit point of A belongs to A. Now we can prove the result.…