Consider the set, A = { 1, 2, 3} what is P(A)? {{1},{2},{3},{1, 2 }, { 1, 3}, { 2, 3},{1, 2, A 3}} В { {}, {1}, { 2 }, { 3 }, {1,2},{ 1, 3 }, { 1, 2, 3}} {{}, {1 }, {2 }, { 3 }, { 1, 2 }, { 1, 3}, { 2, 3},{ 1, 2, C 3}} D {{}}

Q: The set S = {x | x is a continent}. A. S = {N. America, S. America, Europe, Asia, Africa, Australia,…

A: Given:  ( The set S = {x | x is a continent}  Then write the set S

Q: Which of the following sets spans R³? O {(-3,0,2).(0,0,0)} O {(-3,0,2),(5,1,0),(0,-1,1)} O None of…

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Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation,…

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Q: O Intersection of Sets A and B- denoted by ANB is the set of all elements that belong to both A and…

A: We want to find A⋂B

Q: H={b ∣ b ∈ N and 124 < b ≤ 130 } H= { b ∣ b ∈ ℕ and 124 < b ≤ 130} Use the roster method to list…

A: Given the set is  H= { b ∣ b ∈ ℕ and 124 &lt; b ≤ 130} To write the roster method to list the…

Q: Let U = {−4, −3, −2, 0}, V = {a, b, c}. How many subsets does the set U × V have?

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Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

Q: 9) Find the power set of each of these sets, where X, y are distinct elements: (a) {x, y} (b) {x, y,…

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Q: Use the given sets to find D∪(E∩F)D∪(E∩F). U={a,b,c,d,…,x,y,z}U={a,b,c,d,…,x,y,z}…

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Q: Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}  List all the…

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Q: Which of the following sets spans R°? O {(-3,0,2),(0,0,0)} O {(-3,0,2).(5,1,0),(0,-1,1)} None of…

A: Option B is correct

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A = {1, 3, 5, 7, 9), B = {2, 4, 6, 8, 10), and C = {1, 2,…

A: If U be the universal set and A, B, C be subset of U Then  The Union (or join) of the subsets A and…

Q: List the elements of the set. The set of all outcomes of tossing a pair of distinguishable coins or…

A: Introduction: When we perform a random experiment, we obtain more than one possible results. The set…

Q: Use the given sets to find ||A∩B|||A∩B|. U={a,b,c,d,…,x,y,z}U={a,b,c,d,…,x,y,z}…

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Q: List the elements of the set. The set of all outcomes of tossing a pair of distinguishable coins or…

A: A pair of distinguishable and indistinguishable coins are tossed. we have to find possible outcome

Q: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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: Which among the sets is open? a. [0,1) b. {0,...,1/n,...,1/3,1/2,1} c. R\[a,b] d. None of the above

A: The objective of the question is choose the correct option that is a open set.

Q: Which of the following sets spans R? None of these O {(-3,0,2)} O ((-3,0,2),(0,0,0)} O…

A: As per our guidelines only one question can be solved. Solution for the 1st question is given below…

Q: List the elements of the given set. the sets (A n B) U C and An (B U C), where A = {1, 2, 3, 4, 5,…

A: Given, A = {1,2,3,4,5,6} B = {3,4,5,6} C = {1,2,6,7,8} Now,  we have to find A∩B∪C   and  A∩B∪C

Q: 11. For all sets A, B, and C, AN (B-C) C (A N B)– (A N C).

A: We use basic formula of set theory like A – A = Ø  B – A = B⋂ A’ B – A = B – (A⋂B) n(AUB) = n(A – B)…

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: Let X = {a,b,c,d}. List the elements of the set {A :A € P(X) and |A| = 2}.

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Q: 2. Let C and D be subsets of a universal set U, then 2, (C ∩ D) ⊆ (C4D).

A: False

Q: Let A = {0, 1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}, and C = {0, 2, 4, 6, 8} e. Is there a pair of…

A: The given sets are A=0, 1, 2, 3, 4, 5, B=1, 3, 5, 7, 9 and C=0, 2, 4, 6, 8. e. Since the sets A and…

Q: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: Let the universal set, U={1,2,3,4,5,6,7}U={1,2,3,4,5,6,7}, A={1,2,4,5,6}A={1,2,4,5,6}, and…

A:

Q: Let A {p, q, r, s, t}, B = {s, t, u, v}, and C = {p, r, t, u}. Find the set. An C {p, r, s, t, u, v}…

A: See attached file for a step by step explanation to find the required set.

Q: List the elements of the given set. the sets (A ∩ B) ∪ C and A ∩ (B ∪ C), where A = {1, 2, 3, 4, 5,…

A: Given A = {1, 2, 3, 4, 5, 6}, B = {3, 4, 5, 6}, and C = {1, 2, 6, 7, 8}.

Q: 1. Find all sets A such that a. {1} C A and A C {1, 2, 4} b. {1, 2} CA and A C {1,2, 4, 8}

A: see below the answer

Q: Let A = {small, medium, large}, B = {red, black}, and C = {pentagonal, round}. List the elements of…

A: Given : A =small, medium, largeB = red, blackC = pentagonal, round

Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of the elements in each of the…

A: We have to find Cartesian product of part (c) and part (d)

Q: Determine which of the following sets are bases for R3. (a) {(1,0,–1), (2, 5, 1), (0, –4, 3)} (Ъ)…

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Q: List the elements of the given set. the sets  (A ∩ B) ∪ C and A ∩ (B ∪ C), where A = {1, 2, 3, 4}, B…

A:

Q: List the elements of the set. The set of all outcomes of tossing a pair of distinguishable coins or…

A: The answer is as follows :

Q: Which of the following is NOT a subset of 2{a,b} × {a,b} C (b). Ø) C (a,b), (a,b) ) C (a,b}, a) C…

A: Given set

Q: True or False: ϕ is a subset of the set {1, 2, 3, 4} False No answer text provided.…

A: Given, Statement: ϕ is a subset of the set {1, 2, 3, 4}

Q: Let U = {q, r, s, t, u, v, w, x, y, z}, A= {q, s, u, w, y}, B= {q, s, y, z}, and C= {v, w, x, y, z}.…

A: To find  A intersection of B'

Q: ind the complement of the set given that  U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.  (Enter…

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Q: 1. Find the union C1U C2 and the intersection C1NC2 of the two sets C1 and C2, where (a) C1 = {0,1,…

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Q: Which of the following sets spans R°? None of these {(-3,0,2)} O {(-3,0,2),(5,1,0),(0,1,1)}…

A: The solution is given as

Q: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} Use the roster method to list the elements in the set A. A=

A: Given: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} The roster form is given by

Q: Let R1 = { (a,-1), (c,0), (d,1) } and R2 = { (a,-1), (c,-1), (d,0), (u,0), (u,1)} be subsets of A *…

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Q: 3. Consider three finite sets A, B and C. Show that: (a) (b) (c) (AB) x C = (A ×C) \ (B × C ); (AUB)…

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Q: Let A = {H, T} be the set of outcomes when a coin is tossed, and let B = {1, 2, 3, 4, 5, 6} be the…

A:

Q: Find n(A) for the set. A = {300, 301, 302, ..., 3000} %3D

A:

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”.