exercise 1.4. Consider Z/24Z. Determine the set {5 . 1, 5 - 2, ...,5 · 23} =? where z is the class of x in Z/24Z.

Q: Suppose that X,Y and Z are subsets of {1, 2, 3, . . . , 10} and |X| = |Y| = |Z| = 7. (i) Prove that…

A: Given that X,Y,Z are subsets of {1,2,3,...,10} |X|=|Y|=|Z|=7. X∪Y≤10 i)X∩Y≥4 X∪Y=X+Y-X∩YX∩Y=X+Y-X∪Y…

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

A:

Q: Suppose that E1 and E2 are measurable sets. Prove that m(E1 U E2) + m(E n E2) = m(E1) + m(E2).

A: We have to prove that the given statement.

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F open?

A: A set is open if and only if it contains all of its limit points. Also recall that the union of open…

Q: 8. Sketch the sets X = {(x, y) e R :x+y s1} and Y = {(x,y) ER:-1sys0} on R. On separate drawings,…

A: And,

Q: 6. Sketch the set X = {(x, y) E R? : y<x²} on R2. Shade in the set X. %3D

A:

Q: 3. Determine whether the following sets in R3 are linearly independent. a. S = 3

A: Vectors are linearly Independent if there determinant is non-zero. And  Vectors are linearly…

Q: be a collection of sets in S'. Show that we can express U E, as the disjoint union U, Er of sets in…

A:

Q: Let Z = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows:

A:

Q: 2.28 let {Ei} i Ej be a Measurable pairwise dis joint sets. prove that for any bounded set A…

A:

Q: Let G be a a gsoup psove that CGIG)-1and (G:le))-IGI-

A:

Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: 1) Prove that AU(Bnc)= (AUC)N(AUC) 2)Let M-{1,3,n}, find the power set of set M

A: Find the attachment

Q: 3. (a) Prove that A\(BnC) = (A\B)U (A\C) for any sets A, B, C

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Sketch the following set and show if it is open, closed, and bounded or unbounded. 0 < arg(2) < 7/4…

A:

Q: The relation - on the set A = Z x (N - {0}) by (u, v) - (z, w) if and only if wu = zv. Specify the…

A: We will use the relation wu=zv between two elements (u,v) and (z,w) .

Q: Q₂/(a) Let X=(1, 4, 5,7, 8, 9) and o= {(1,4),(4,7, 8}}, show that whether o is: (1) a subbase for a…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 5) Let A= (2,3) U {4} be a subset of R with the standard opology. Find Ə(A).

A:

Q: Prove that Z ≈ E*, where Z is the set of integers and E* is the set of positive even integers.

A: To prove:

Q: Q) Make up a Kelly table for set G= [1,-1, i,-i} with respect to multiptication and then explain…

A:

Q: Suppose that |x| = n. Find a necessary and sufficient condition on r and s such that (x") C (x*).

A: Given,

Q: A relation R defined on the given set A will satisfy

A:

Q: 7. Let E and 0 the set of even and odd integers, respectively. Prove that {E, O} partitions Z.

A:

Q: 5. Show that the set {e" : n e Z} is countable. (Hint: Use the function f(n) = en and show it is 1-1…

A:

Q: Let G=(V, E) be a finite

A:

Q: ( Prove that the set {a E R2: a2 ... Prove that the set {a E R2: a2 not equal to 6} is open.

A: Let the set is A=a1,a2∈ℝ2:a2≠6 The objective is to prove that the set A is open.

Q: 2.6.4 Let A CR be a non – empty set. Suppose that A is bounded above. Let U = {x E R|x is an upper…

A:

Q: Let S be the set of integers. If a, b E S, define aRb if ab &gt;= 0. Is R anequivalence relation on…

A:

Q: (a) Let A be a subset of R". Show that (A = (A°)°.

A: WE proved it using Claim 1 and Claim 2.

Q: 2.12 let A and B bounded sets For which there is an ε >o such that la-blze for all ac A, be B .…

A: Consider A and B are bounded sets.

Q: Let G = Z, O Z, H = {(0, 0), (2, 0), (0, 2), (2, 2)}, and K = ((1, 2)). Is GIH isomorphic to Z, or…

A:

Q: Identify all nonempty set/s from the following A = {x|x € N, 2x + 7 = 3} B = {x|x € Z, 2x + 7 = 4} C…

A:

Q: Let R be an equilene relation defineed an IN as follows ! 2-8(x)ENIN Y-y alivisible by3}

A: It is given that let r be an equivalence relation defined an 1n as follows R={(x,y) belongs to N*1N…

Q: 1. Suppose R and S are symmetric relations on a set A. Prove that Ros is symmetric if Ros=SOR

A: Given:  To prove R and S are symmetric relations.

Q: 2. Let f and g be permutations. Show that the fgf¯ is the same as the order of g. order of h =

A: our objective is to prove the result

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: 2 Let A be a fixed nonempty subset of set X and I= {Bc X | A Z B}. Show that (X,I) %3D is a matroid.

A:

Q: If A = (0, 1) n Q, then {x; x E (0, 1)} is the set of all cluster points of A. Select one: OTrue…

A: Given A= (0,1) ∩ Q . Then the set of all cluster points of A is  = {x: x ∈ [0,1]}

Q: 11.2. Find images of the following sets under the mapping w = 1/z: (a). {z :0 < |z| < 1, 0< arg z <…

A:

Q: Let 9-(a: a€R}, then T is Borel algebra.

A: Clearly the measure of the set is =0 .

Q: 2. Write a preference E on R as a subset of R', where a bundle a E Rª is at least as good as a…

A: To write: A preference ⪰ on ℝ+2 as a subset of ℝ+4, where a bundle x∈ℝ+2 is at least as good as a…

Q: Let f and g be any permutations. Show that the order of h=fgf^(-1) is the same as the order of g.

A:

Q: 3. Prove if x is an isolated point of a set S, then x E bd S.

A: Since you have posted a multiple question according to guildlines I will solve first question(Q3)…

Q: 2) let A be a finite set and a EA.Lf a EA is not a maximal element of A,then a has an îmmediate suc…

A:

Q: An operation * on a set S is a relationship that assigns to some ordered pair of elements of S a…

A: We have to tell about the statement is whether true or false

Q: What is the characteristic function of set A = {1, 3, 8, 12}? Prove A U (BnC)=(An B) U (An C), given…

A: Given:A=3,6,8B=4,6,9C=4,8,9To prove:A∪B∩C=A∩B ∪ A∩C

Q: 3.3 Let 11 and ra be distinct points in the metric space (S, d). Verify that there are open balls…

A:

Q: 4. Let E be a measurable subset of [0, 1) and E+y for y E [0, 1) be a translation modulo 1 of E.…

A: Given that E is a measurable set. Consider the set E+∘y=x+∘y : x∈E where x+∘y is defined as…