Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x ∈ X and y ∈ Y and (y – x) is divisible by 6}

Q: List all the subsets of {x, y, z, y}.

A:

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: List all the subsets of the set                   { –1, 0, 1 }.

A: All subsets of {-1,0,1} is:

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A: This is a problem of Real Analysis and Topology.

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x EX and y EY and (y * –…

A: R has three elements.

Q: List all of the subsets of (x, y, z).

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Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: 2. a. List all 3-combinations for the set {x1, x2, x3, X4, Xs}. Deduce the value of (,). b. List all…

A:

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: True or False The intersection of two sets is always a subsetof their union

A: To check the statement

Q: Let A=(1,2,3,4), B=(00,01,10,11), C=(x,y,z). f1 = {(1,00),(2,01),(3,01),(3,10) (4,11)}. %3D f2 =…

A: Given that:

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

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

Q: Consider the poset ({2, 4, 5, 10, 20}, [). What are the upper bounds and lower bounds of (5, 10}?…

A:

Q: Show

A: We prove this statement by using definition of Borel Set.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A:

Q: If a set A has 63 proper subsets, what is |A|? *

A: Solution...

Q: Let १ १G,१ी, (३,5) , (3 ), (4,2 ), ( 3 4) 5 %3D and 4. १,०) (2) (৬,), (,০), (3,) 3 %3D which of the…

A: The solution of the problem is given in the next step.

Q: Determine whether the points are coplanar.(1, −5, 9), (−1, −5, 9), (1, −5, −9), (−1, −5, −9)

A:

Q: Use the roster method to list the elements in the set: {x|x is a whole number less than 4}.

A:

Q: Let A, = {..., – 2, – 1,0,1,..., i}. Find ỦA, i31

A: First we find A1, A2, A3,...An, then find union as in next step.

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 cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

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

A: Write the given interval in inequality form as follows: 4<x<10

Q: denotes the set of subsp

A:

Q: Let A=(1,2,3,4}, B=(00,01,10,11}, C={x,y,z}. f = {(1,00),(2,01),(3,01),(3,10) (4,11)}. f2 = {(1,x),…

A:

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

A:

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

A:

Q: Let result space Q, = {3,5,6,7} and results A = {3,6}, B = {3,6,7}, C = {6,7} given Calculate:…

A: Set: In mathematics, a set is a collection of distinct elements. It is usually denoted by A, B, C…

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В %3 {3, 1, 9, e, а, с, 0}, and C 3D {2, с, 10, 9, 8, —4,…

A: solution of the given problem is below...

Q: Let X = {1,2,3,4} SUCH THAT TX = {4, {2},{1,2},{2,3} , {1, 2, 3},X}: AND Y = {1,3,4} C X, THEN TY =

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A:

Q: Let A, B and C be three sets such that: Set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15} and…

A: We have find answer.

Q: Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8}. (Use the roster method to…

A: Complement of a set: It includes all those elements of universal set which are not in that…

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x e X and y e Y and (y –…

A: Let X={1,2,3,4,5} and Y={7,11,13} are two sets. And R={(x,y): x ∈X, y∈Y} and (y-x) is divisible by 6

Q: Give the inclusion – exclusion formula for four sets where A U B U C U D in terms of sizes of in

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 O XT) is neither…

A: Option 1 is correct.

Q: Let 5- {-3, -1, 0,1 V5,4,3). Determine which elements of S satisfy the inequality. (Enter your…

A:

Q: Assume that a fair die is relled. The samnple space is1, 2, 3, 4, 5, 6| and all the outcomes are…

A: If a fair die is rolled, then we get sample space as  S={1,2,3,4,5,6} Let E denote the outcome of 6…

Q: Let f : {1, 3, 4} → {1, 2, 5} and                   g : {1, 2, 5} → {1, 3} be given byf = {(1, 2),…

A: The function f and g can be denoted as follows.

Q: Suppose that the set A is such that P(A) = {0, {3}, {5}, {6}, {3,5}, {3,6}, {5, 6}, {3,5,6}}. %3D…

A: (a) Given for set A, PA=ϕ,3,5,6,3,5,3,6,5,6,3,5,6 We have to find the set A Hence, A=3,5,6 (b) Given…

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: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

Q: Let X (1, 2, 3, 4, 5) and Y (7, 11, 13) are two sets. find R ((x, y):xEX and *yEY and (y- x) is…

A:

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

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”.