3. Show that if X-ty to a constant morphiam in a connected category, then there exist's a unique constant morphism Y. → Y such that hof=f.

Q: All the possible relations on A {1,2,3} is equal to i. i. 8 relations 9 relations Non of these iii.

A: The number of relations on a set of n elements is given by 2n2.

Q: 8. Consider the binary relation R defined on (N* x N*) by: V (x1. Y1). (X2. Y2) E N* x N*, (x1. Yı)…

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Q: 1- Which of the following is a homomorphism? a)O f:Z→Z, f(x) = x+2 %3D b) O f: Z12 → Z30, ƒ(x) = 20x…

A: Consider a function    .Then f is a homomorphism if and only if  . .

Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A: Since you posted a multi sub part question but according to guidelines we will solve first three sub…

Q: 3. ** Prove that the relation D given by xDy iff / EZ ΕΖ (namely, xDy if x is a divisor of y), on…

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

Q: Let A = follows: For V(a,b), (c,d) = A x A, (a,b)R(c,d) ⇒ a ≤ c and b ≤ d {0,1,2} and the partial…

A: a. The Hasse diagram is shown below.

Q: 1. Let T be a group of all invertible 2 x2 matrices of the form Where a.b.C ER and ac+0. Let / be…

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Q: . Let C = {0, 1, 2, 3} and f : C → C, g : C → C with f = {(0, 2),(1, 2),(2, 3),(3, 0)}, g = {(0,…

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

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Q: Suppose g: U →→ C is a holomorphic function on a domain U. Suppose a EU and the disc {z € C: |za| ≤…

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Q: Consider the relation being described by the following arrow diagram. Which of the these statements…

A: (i) It is given that ;      S = {6, 7, 8}  and  T = {2, 4, 6} And the relation between S and T is :…

Q: 6. Give an example of a relation R on A = {-1, –3, –5} such that: (a) R is both symmetric and…

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Q: Justify if it is true: If T:V → W is a monomorphism, then V = T(V)

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Q: Show that the function f: [1, 2] → [1,8], f(x) = 7x - 6 is a bijection. What relationship exists…

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Q: 2 Relations For the following relation R over the integers, prove whether R is or is not: 1.…

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Q: 11. Is there a bijection f NZ? Justify your answer. 12. Give an explicit description (as a set of…

A: According to bartleby guidelines we do only first question and next questions can be reposted…

Q: 5*. Suppose that 0: G -+ H is a homomorphism. Prove that (a) (a")= (x)" for all positive integers n.…

A: To prove the properties of group homomorphisms

Q: Let f: X → Y and g : Y → Z be arbitrary maps of sets (a) Show that if f and g are injective then so…

A:

Q: 2. Consider morphisms f: A → B, g: BC, h: CD, k: DB, j: BC, t: A → C in a category C so that g is an…

A: Given: Morphisms f:A→B, g:B→C, h:C→D, k:D→B, j:B→C and l:A→C in a category C, where g is an…

Q: al let (xt) betopology space and BCY then B is closed in y iff there is closed set CinX st B-COY

A: Let (X,Γ) be topology space and B⊂Y To Prove: B is closed in Y iff there is a closed set C in X s.t…

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: f for ƒ : R - {2} → R- { 5} indicated by f (x) =(5x +1)/(x -2a), a bijection can be made from [0, 1)…

A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: 1. This is one 1-1 correspondence between Z and I. f : I → Z f(n) = { n = 1, 3, 5, - …. 7, n = 2, 4,…

A: f(n)=n-12n=1,3,5,7,⋯-n2n=2,4,6,8,⋯

Q: (1) Define relation R on the real numbers, R, by xRy if and only if [x] = [y]. Determine which of…

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Q: 1 If MR =: 1 lo 1 1., then the relation ol 1 Ris Reflexive Transitive Anti-symmetric Symmetric

A: To find: The type of relation R. Concept used: Reflexive: If all the diagonal element of MR is 1,…

Q: Consider the relation R on R defined by (x, y) E R if and only if |æ – y| = ||x| – ly||- This…

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Q: Let T be an operator on an innner product space V, and suppose that ||T(x)|| = ||x|| for all x in V.…

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Q: (a) Suppose S is a subset of positive integers, ZZ. If |S| ≥ 3, prove there exist distinct z and y…

A: (a) Given that S is subset of  such that Observed that any positive integer is either even or odd…

Q: et SCN be the set that contains exactly all prime numbers, and let RC S x S be the relation efined…

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Q: Define g : (-1, 1) → R by g(x) 1- x2 " Show that |(-1, 1)| = |R| by showing that g is a bijection

A: Concept Used: For a function f:A→B If f is a bijection, then |A|=|B| Consider the function g:(-1,…

Q: ´f(1) f(2) T: R3 [æ] → R* is given byT(f) = f(3) . Which statement about T is correct? f(4). O Tis…

A: Isomorphism T or F

Q: . Prove that the shift o is a homeomorphism.

A: To, prove that σ is homomorphism we will show that the inverse image of open set is open. So, the…

Q: 5. Prove the following statements. (i) Let f: A B and g: B-C be two functions, If g of is onto, then…

A: