Check whether The basis of folowing set not is or 2. 2.

Q: Let A, B and C are sets. Prove that <= is transitive

A: For proving transitivity we need to show that if A&lt;=B and B&lt;=C then A&lt;=C

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

A:

Q: Let (X,T) be a toplogical space, A, BC X. Show that АС В Ас в, АсВ. 介

A:

Q: {(x,a),(x,b),(x,c), (y,a),(y,b),(y,c)} is the Cartesian product AXB of two sets given as A = {x,y} B…

A: Let A and B are two sets. Cartesian product of A and B will be denoted by  A×B                A×B…

Q: Determine whether the set spans all of M2. Justify your answer with your work and/or written…

A:

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

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

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

A:

Q: Using contradiction method, prove that for every nonempty sets A and B, An (B- A)=0.

A: The given problem is to prove the following set identity using the contradiction method.

Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

A:

Q: Use an element argument to prove that for all sets A and B, (An B) U (AN BC) = A. %3D

A: I have proved that sets on both side are subsets of each other and ten concluded that they are equal

Q: For all sets A , B and C A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C )

A:

Q: Consider S to be the universal set. Let X = (AUB) nC and Y = (AnT)U (An B). %3D Write out the…

A:

Q: Đ A is a closed set.

A:

Q: Determine whether or not the set s ]日) 2 1. %3D 3. is a basis tor Rš.

A:

Q: Let X = {a, b, c, d, e} and let T= {X, ø, {a}, {c,d}, {a,c,d}, {b,c,d,e}}, then * (X, T) is not…

A: Option 2 is correct.

Q: State true or false with brief justification: L1[a,b] is a reflexive space

A: We use the Theorem: Let X be a separable normed space. If the dual space X* of X is non-separable,…

Q: Prove using the properties of set operations: a. B-A and An B are disjoint.

A: Solution

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

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: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

A:

Q: Determine whether the set spans all of M2. Justify your answer with your work and/on written…

A:

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Express (4, 10) as a set {x : |x − a| &lt; c} for suitable a and c

A: Write the given interval in inequality form as follows: 4&lt;x&lt;10

Q: Prove the following theorem directly. 'Let B, E,W be sets. If B Ɔ W, then BU E WUE"

A: Given B, E and W are three sets .

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

A:

Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: What is meant by Idempotent law in sets?

A:

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: List all the possible subsets of set G, where G = {-7,m,z}- %3D

A:

Q: 10. Determine which sets are a basis for R². (a) (b) © {[2] [9] [17]} {8.8} (Ⓒ) {B} {[]+[2]}

A: To identify which of the given set is basis for R2

Q: Use element argument method to prove that if A and B are sets such that P(A) ≤ P(B), then A ≤ B,…

A: I just used the definition  Of power set and subset of set

Q: Determine whether or not the set {(2, 21, 0), (1, 2, 5), (7, 21, 5)} islinearly independent over R.

A:

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

A:

Q: What is the complement of the set X? How is it denoted?

A: Universal set is always given to find complement of a set. Complement of a set 'X': It includes…

Q: Đ A is a closed set.

A: We prove by using the result that intersection of two closed set is closed.

Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

A:

Q: Exercise 1.5.5. (a) Why is A- A for every set A? (b) Given sets A and B, explain why A~ B is…

A: (a) To prove that, A ~ A for every set A.

Q: Which of the following sets are closed under multiplication?

A: Given: (a) The set of all prime numbers. (b) The set of all even numbers. (c) The set of all…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: {(x,a), (x,b), (x,c), (y,a), (y,b).(y,c)} is the Cartesian product AXB of two sets given as A =…

A: our objective is to find A

Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and…

A:

Q: Prove (((LOM)-N) U(N-(LUM))) < (LU (MUN)) L, M, N are sets.

A: To prove: L∩M-N∪N-L∪M⊂L∪M∪N

Q: Explain why the set is not a Basis. S = {(2,3), (6,9)}

A:

Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.