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: Prove or give a counterexample to the following statement: for any relation R both R and RoR always…

A: Suppose R is a relation on a set X, then the transitive closure of the relation R is the smallest…

Q: Is the relation R on X is reflexive, symmetric, weakly antisymmetric, antisymmetric, transitive?…

A:

Q: Prove that for  1 < p < infinity   lp(F) is banach

A:

Q: 5. Let a E G be fixed. Define y: G → G by p(x) = axa-1 for all x E G. Prove that p is a…

A: To find - Let a∈G be fixed. Define ψ:G→G by ψx=axa-1 for all x∈G. Prove that ψ is a homomorphism.

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

A:

Q: Determine which of these relations are transitive. The variables x, y, x', y represent integers. A.…

A: Note: As multiple questions have been posted, so only A is solved according to QnA guidelines.…

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

A:

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…

A:

Q: 2. For TEL(V, W), prove that T is injective if and only if 7* is surjective.

A: T is injective if and only if T* is surjective.To prove this statement, we need to show that T is…

Q: The function f: x 1-> a + b cos x, is defined for 0sxs 2n. Given that f(0) = 10 and that %3D n)= 1,…

A:

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

A:

Q: 4. Consider the following relations R on the integers Z. For each of these relations, say whether…

A: For the solution of the problem follow the next steps.

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: (a) x and y are in the same major. (b) x and y have the same last name. (c) x and y are taking a…

A: See the attachment

Q: VIII.3. Is there a mistake in the following proof that any transitive and symmetric relation Ris…

A: Yes there is a mistake. That Symmetric and transitive relation doesn’t imply reflexive. in the…

Q: Let V = V(r - y) C A. Consider the morphism o: A' → V given by o(t) = (t,t). (a) Show that o is a…

A: Given: V=Vx3-y2⊂A2 ϕ:A1→V by ϕt=t2,t3 To do: Show that ϕ is a bijection but not an isomorphism.…

Q: Let A = {x | 5x + 1 E Q} and B be the set of all even integers. Prove that A and B have the same…

A:

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

A:

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: 1. For each of the following relations, determine whether it is (a) reflexive, (b) symmetric, (c)…

A:

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

A:

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

A:

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: . 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: With regard to composition of relations, If S and R are both anti-reflexive, then  s∘r is…

A: S&amp;R both are anti- reflexive. Therefore There is no common elements in theses two sets.

Q: 6. Given the following relations on the set of all integers where (z,y) = R if and only if the…

A:

Q: 1. For each of the following relations, determine whether it is (a) reflexive, (b) symmetric, (c)…

A:

Q: 1. Let & be a connected category and hi Z→X and f Y. X= ง and g are Prove that if f ouch that f‡g,…

A: Given that:Let  be a connected category and  such that .To prove: If f and g are  constant morphisms…

Q: Prove or disprove the relation C on Z defined by C = {(x, y): x=y (mod 5)} satisfies the two…

A: I just used the definition of congruence and divisibility

Q: 3. (a) For a given set A, consider the relation R= { (X, Y)|Χ ΕΡA) Υ ΕΡA) , and X Y) Show that R is…

A: Partial order relation

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: Show that the glosp of bncar bijections ftom f5 faom f5 whes fis afjeld in isomaphic with GLI5f)

A:

Q: A relation < is defined on R by x < y if and only if there exists k E N such that x = y + 3k. Prove…

A: Partial order relation

Q: 2. Suppose f is holomorphic in an open set UC C and a € U. Show that for any integer n ≥ 0 there is…

A: Given f is a holomorphic in an open set U⊂C. Let a∈U. Now, we form a new holomorphic function…