List all elements of A that are related to 5. (5 S x). This is the class of 5 denoted by [5].

Q: How many functions [5] to [3] are onto?

A: Solution

Q: • x² – 3 = 0 x2 – 3x = 0 x² + 4x = -4

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: The set G = :a is closed under addition %3D 0 2a

A: Use the closure property of addition.

Q: Find k such that 2x = ekx for all x.

A: To find k 2x=ekx

Q: Represent in the Argand Diagram all such z for which |z+ 12 - 5i| < 6

A:

Q: F, there is a disconnection A, B of F such that x E A and y E B. 8.X. If C1, C2 are connected…

A: We use the fact that a set X is connected if there is no continuous function form f from X to Y=…

Q: Consider the set A = {1/2^{n-1}: n\epsilon \mathbb{N}}. Show that Inf(A) = 0. WITHOUT USING LIMITS

A:

Q: Find the value of c such that enc = 7 c= In

A:

Q: relation R on Z defined

A: Given, a relation R on Z defined by mRn ⇔ 7|(m − n) for all m, n ∈ Z.

Q: The characteristic of Z6 x Z, is 18.

A:

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

A:

Q: Compute |A| for the following:

A: We have to compute A for the following given matrix: A=210121012 We know to determine the…

Q: Prove that d24 and s4 are not isomorphic. List elements and there order.

A:

Q: Notice that h is definec this.)

A:

Q: Suppose that E is an extension of F of prime degree. Show that, forevery a in E, F(a) = F or F(a) =…

A: Let E be an extension of F of degree p (prime) =&gt; [E : F] = p Here we will use tower property to…

Q: Given a relation R on Z defined by mRn ⇔ 3|(m −n) for all m, n ∈ Z. Find the equivalent class…

A: We have the relation defined by mRn⇔3/m-n Now ,we need to find the equivalence class determined by…

Q: Suppose  v,w is an element of V. Explain why there exists a unique x which is an element of V such…

A: Suppose v, w is an element of V. Explain why there exists a unique x which is an element of V such…

Q: Give an example of a closed subset S of R^2 such that conv S is not closed

A: An example of a closed subset S of R2 such that conv S is not closed is given below.

Q: Prove that all elements in S are multiples of 3. by Structualindrction 3ES X,Y ES > (X y )ES

A:

Q: Suppose T: R + P, has an action on a

A: Given, And

Q: Show that for every x E R, there exists an n EN such that <x<n.

A:

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

A:

Q: Find the elements of A, where A = {x|8 >x> 1} 1. 2. Find the eiements of the binary relation from A…

A:

Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: O Prove that the composition óf önlo

A: # we are entitled to solve one question at a time ,please resubmit the other question if you wish to…

Q: For any set A and any ≥0, there exists an open set O such that A CO and m* (0) ≤m* (A) + €.

A:

Q: For each subfield S of Q[i, z], determine Auts(Q[i, z]).

A:

Q: Let S = {n + m√2 : n, m ∈ Z}  To prove that the sum of any two elements of S is an element of S.…

A: Given: S=n+m√2:n,m∈Z  (a) Let a+b2∈S for all a,b∈Z and let c+d2∈S for all c,d∈Z Add both these…

Q: Find the elements of Z24 of order 8. (Hint: o(1)=24)

A:

Q: Let K be an extension of be an algebric element o 2 F Show that a ² is algebr

A:

Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: (b) There exists LE R such that L4 Size(O(n)).

A: Given below clear explanation

Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

A: In this question, we use the definition of Riemann integral to check the function H(x) is Riemann…

Q: Question 3. Consider the relation R(ABCD) with AB as a candidate key, choose the FD so that R should…

A: Given the data:

Q: For any k = 1, 2, .... n, find E T₁+T2+ T₁+T2+ ... + Tk + In,

A:

Q: (1) For each member of your group record their response to: Give an example of a polynomial and an…

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

Q: To which of the following does the Well-Ordering Principle directly apply? x(x + 1) x E Z 2 z*} A. O…

A:

Q: Represent in the Argand Diagram all such z for which |z − 5i| > 8

A: Any complex number:z=x+iy can be represented in the argand plane. For any complex number:z=x+iy, it…

Q: Which of the following is isomorphisma f: (R, .) → (R, .) where f(x) = Inx this option O None of…

A: Lnx is not a function and second ome is not onto

Q: For each given value of n, find all homomorphic images of Zn.   n = 6

A: To find all homomorphic images of ℤ6

Q: (a) Show that for x > 0, 1 5a' < In(1+ x) < |

A: As per guidelines, we will solve only first part. Kindly repost other part separately.

Q: Use index notation to prove the following relation: ахb.с%3а:(bxс) — сха. b.

A: Let,a→=a1i→+a2j→+a3k→b→=b1i→+b2j→+b3k→c→=c1i→+c2j→+c3k→

Q: For any x E R, there exists n EN such that x < n; ylgn ihi

A: We have to state whether given statement is true or false.

Q: Given a relation R on Z defined by mRn 3|(m – n) for all m, n E Z. Find the equivalent class…

A:

Q: Let X be an infinite set. Define u : E = P(X) → Ř by %3D if A is finite µ(A) = 1 if A is infinite.…

A: Let X be an infinite set and ∑ =P(X) Let μ=P(X)=∑ → ℝ is given by μ(A)=0if A is finite1if A is…

Q: For each xe X and a nbd: U(x) of x there exists another nbd.

A:

Q: Consider the subset G {r• /2: x € Z} of R. Show that G is closed un- der addition.

A: The given subset is: G= x·2 : x∈ℤ

Q: Let A ∈ Mn×n(F). Under what conditions is det(−A) = det(A)?

A: In determinant the scalar quantity is taken common from a single row or a column.

Q: Show that Oa = {a} if and only if a e Z(G).

A: For a∈G, Oa denote the orbit of 'a' under the conjuction action.The orbits under the conjucation…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.