Sets, Relations and Functions 1. The sets R, S, and T are defined as follows. R = {x € Z]x is divisible by 2.} S= {y € Z]x is divisible by 3.} T = {z € Z]x is divisible by 6.} a) Es R CT? b) Es T C S? c) Es R US + T? Note: In all cases, argue your answers.

Q: 2. Find sets A, B, C, D such that the sets (AN B)U (C\ D), ((An B) U C) \ D, An(BUC) \ D, An(BU(C\…

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Q: 1.) The Universal Set, U, is defined by the uppercase letters of the English alphabet. Set A…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: Consider the following sets: U = {2, 3, 4, 6, 8, 9, 10, 12, 14, %3D 15} |А%3D {3, 6, 9, 12, 15} В…

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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: Which of the following statements are set identities? That is, which of the statements are true for…

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Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: 4. Prove or disprove For all sets A. B and C. if A OC-0,then A. B and Care your answers as ar AUD,…

A: The given statement is FALSE.

Q: Let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;…

A: given let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;…

Q: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

Q: (4.2) For sets A, B and C, prove that (An B) x C = (A x C) n(B x C).

A: Here we have to prove that (A∩B)×C=(A×C)∩(B×C)

Q: Let S={a, b, c, d, e, f, g, h, i, j} be the universal set, A={c, e, f, h}, and B={a, b, c}. Find the…

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Q: Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it…

A: Truth table for the symmetric difference is,

Q: 10) let R and S be two relations from A to B, then the set = { ( a, b) e A×B:( a.b) ER} is

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Q: How would a mathematician say: “Take the set {s,u} and give it the name G” Let D = {u,j}. Is j a…

A: 1. Let, G=s,u 2. Consider a set D=u,j. A set X is a subset of another set Y. If all the elements of…

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

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Q: Another operation that can be defined on sets A and B is the difference of the sets, denoted by A -…

A: The given universal set is                                       U={1,2,3,4,5,6,7,8,9}    and the…

Q: If A = {a, b, c, d) and B = {c, d, e, f, g}, then n(A U B) = n({a, b, c, d, e, f, g}) = 7, n(A) = 4,…

A: We have to find

Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: 1. (a) (i) What does nMn N] = 0 imply about sets M and N? (ii) What is implied about sets A and B if…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: If A and B are sets; Aºand Bºdenote the complements of the sets A and B, then the set (A – B) U (B –…

A: Given:- If A and B are sets; Ac and Bc denote the complements of the sets A and B, then the set (A -…

Q: State whether each of the following statement is true or false. Justify your answer.(i) { 2, 3, 4, 5…

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Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

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Q: Which of the following sets is open in (R, Tu)? OR-(Q-Z) OR-)"2n² :ne N} [2,5) O 12,5) U (1, 7)…

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Q: Let R, S, T be subsets of the universal set U such that n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

A: We will draw a Venn diagram using the given information: n(U) = 64, n(R U S U T) = 45, n(R) = 22,…

Q: 1.         Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U =…

A: From the given information, the given sets are:

Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: Which of the following sets is closed in (R, Tu)? O a. { ne N}U{2} 72 2n O b. Q-N c. O c. [2,5) U…

A: Determine the meaning of ℝ, τu. Now, go with each option and check which is correct.

Q: Find the intersection of the sets. {r, e, a, l}∩{l, e, a, r}

A: Given:A=r,e,a,lB= l,e,a,rIntersection set:The set containing all elements of A that also belong to…

Q: For nonempty sets A, B, and C, |A| <= |B| and |B| <= |C|, then |A| <= |C|.

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Q: True or false 1.The intersection of two sets is the set of all the equal elements that belong to…

A: Since you have not mentioned the questions to be solved, so we are providing you solutions for first…

Q: Another operation that can be defined on sets A and B is the difference of the sets, denoted by A −…

A: First we have to find B' (complement of B)

Q: (a) By contradiction, prove that V r, y € Z, if ry is even and y is odd then x is even. (b) Show…

A: (a) Given v x,y ∈Z,     &amp; xy is an even integer with y is odd.     To show x is even.      Let…

Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: This question refers to unions and intersections of relations. Since relations are subsets of…

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Q: 3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define…

A: Set equality proof

Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: The given sets are: A={-2,2,3,5} and B={2,3}

Q: (2) For the following three set definitions, describe the ele universal set is the entire English…

A: Given,  Set 1: A, E, I ,O, U, Y Set 2: A, B, C, D, F Set 3: I, J, K, X, Y, Z

Q: Show that (B - A)U(C- A) = (BUC)- A 1) Using a Venn diagram 2) Using the definition of equal sets

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Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

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Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: point the step in the argument that is not valid and explain why ? Theorum: For all sets A,B   A’∪B’…

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Q: 1. For any sets A, B, and C; the distributive law states AU (B nC); that is a. (A U B) n (A UC) b.…

A: Let A, B, and C are three sets

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

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Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: A={-4,4,7,9}B={4,7} A×B=-4,4,-4,7,4,4,4,7,7,4,7,7,7,4,7,7,9,4,9,7

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: For Exercises 37-40, reler to sets A, R, C, Xx, Y, and Z amd find the umiom or Intersection of sets…

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Q: i) If X,Y,ZX,Y,Z are finite sets, then                               |X∩Y∩Zc|=|?1∩Y|−|X∩Y∩Z| where…

A: if X , Y , Z are finite sets (i) X∩Y∩ZC=?∩Y-X∩Y∩Z it is known that X∩Y∩ZC=X∩Y-X∩Y∩Z

Q: Consider the sets to answer the following questions attached: A = {a, b, c, d, e, f, h, j} B = {a,…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.