Let the Universal set be U = (1, 2. . 20)., A= (1,6.11,19) and B = (6, 11, 14, 7) fa-8) (1) = '(A@ (11) = fa-5 (19) =

Q: How many subsets of the set {1,2,3,4,5,6,7,8} have cardinality 3 or less?

A: Here we need to find how many subsets of the set A={1, 2,3,4,5,6,7,8} have cardinality 3 or less so…

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: 1. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it…

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Q: The cardinality of { Ø, 1, 2, 2, {1, 2}} is

A: We need to find the cardinality of { ϕ, 1,2,2,{1,2}}.

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

A: We will find out the required solution.

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

A: The union of two sets is composed of elements of the same two sets.

Q: If AnB is pathwise connected set.  then A and B are:  a. Pathwise connected sets b. Not pathwise…

A: Pathwise connected means any two points in that set can be join by a continuous function. Roughly…

Q: What is the class width (i) if one of the class interval is 18-26?

A: If class interval given is 18-26 The class width is difference between upper interval and lower…

Q: => find fundamental set of Se yo=-3x²e-3x ZR 7:

A: We have to find the fundamental set of solution.

Q: the sets  [0,1] and  [0,1/2)∪(1/2,1] have the same cardinality, give an explicit bijection to show…

A: We will define a bijection from the set J  = [ 0 , 12 ) ∪(12 , 1]   to the set I =0 ,1   First we…

Q: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

Q: Prove that [2,5] and (3,4) have the same cardinality.

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Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

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Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: Let (x, eA) be a measurable space, £: X (-∞, w) and 9:* (-∞0, ∞o) are measurable. Prove that the…

A: Given that X,A is a measurable space. The objective is to prove that the sets  {x∈X:f(x)&lt;g(x)},…

Q: Show that the o-algebra B of Borel sets contains all F,-sets.

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Q: The relation by a = b (modn) is Partial Order Relation Ture O False O

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Q: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

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Q: denotes the set of subsp

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Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

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Q: Deteimine the set of vectuns sci, iti), (1tiyzi)f linealy dependent or linenly Indefendteut? is

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Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: Prove that [0,1] has the same cardinal number as [0,2] U[7,9].

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Q: Show that the N and the set {1,3,7, 15, 31, . . } have the same cardinalit

A: To show N and the set S= {1,3,7,15,31...} have the same cardinality, we need to show there is a…

Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: Prove that derived set of a bounded set is also bounded.

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Q: Let {S,}EN is a disjoint seqeuence of measurable sets , then: US, µ(S,)

A: Given a statement

Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has 150 followers and a follower of Jim follows Jim and 149 others. Let the set S is…

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: 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: Let'Y be the set of f bleod types B+ Hat type Connot donate blood to.

A: Here, X is the set of blood types AB- can donate blood. AB- can donate blood to AB- and AB+ Hence,…

Q: There are 6 towns {A, B, C, D, E, F} with the following one way street relation {(A, B), (A, C), (B,…

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Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: a) Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets…

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Q: Prove using Venn diagram that An (B U C) = (A n B) U (A n C)

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Q: Suppose Ak,., A2 , A1 and B are points on R" Prove that if {A1 , A2, .. Ak} is an independent linear…

A: proof :- A1,A2,...Ak are linear independent set ⇒c1A1+c2A2,...ckAk=0  where c1=c2=...=ck=0…

Q: Find the cardinality of the set {x|x is an even whole number less than 10}.

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Q: Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection…

A: Yes, the sets 0,1 and 0,12∪12,1 have the same cardinality.

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

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

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: 2. Let U = {a, b, c, d, e, f, g, h} be the universal set, and let A = {b, c, d, f, g}, B = {a, b,…

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Q: Determine how many one-to-one correspondences are possible between two sets, {p, s, z, w, v} and {1,…

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Q: Suppose R is a relation defined on the set A = {1, 2, 3}. If R = {(1,1), (1, 2), (2, 1), (2, 2), (3,…

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Q: Let P={1.2,3,4,12,36} and the relation set R={(1,1)…

A: The objective is to show that (P,R) is a poser. Represent the relation using the diagraph and then…

Q: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: A = {(0, 0), (0, 1), (0, 3),…

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