The number of elements in As is O 120 O 25 O 5 O 60 Which of the following is correct? * O None of these O U(14) is isomorphic to S3 O U(14) is isomorphic to U(7) O U(14) is isomorphic to U(12)

Q: The generators of Z,, are: (1,57,811) O (13,7.11) O ass711) 'O 05711) O O O O

A: we have to find generators of z12

Q: If * is a binary operation in A then Select one: O a. A is closed under* O b. A is not closed under…

A:

Q: Determine if g 15 is a primitive element for Z3 if the following is the output for powers of 15 from…

A:

Q: (9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts…

A: 9.For  be positive integers, a weak composition of  into  parts is a -tuple  of nonnegative integers…

Q: Asume that the binary operation a * b = a + b - 5ab is defined on Z. Which statement is NOT correct?…

A:

Q: What does the K stand for in Kn? (Finite)

A:

Q: Using the natural homomorphism(which takes every integer to its equivalence class) of Z onto Zk for…

A: The idea is to reduce the equation mod 5

Q: (1234 56 314562, Let o = find o5 (1234 56 314562, (1234 56) 612435, O None of them 1234 56) (124365…

A: Just write the given permutation in cycle form and then compute the order of permutation and you'll…

Q: Find an integer n such that U(n) is isomorphic to Z2 ⊕ Z4 ⊕ Z9

A:

Q: 1. SCP or SSxy" 2. SS,=. 3. SS,=, 4. Calculate the Pearson product moment correlation between X and…

A: Since you have posted a question with multiple subparts, we will solve first 3 subparts for you. To…

Q: Let i be a positive integer and A; =] -i+1,1[. Then N,A;= O 10,1] None of these O 10,1[

A:

Q: On the operation on S={A,B,C}. given by the table A В C A C A В В A В С В А С Select one: a. not…

A: Definition:- A operation * is said to be commutative if for any two elements say A,B  A*B=B*A holds.…

Q: Let i be a positive integer and A; =] - i+1,1 [. Then N A= None of these O 10,1] O 10,1[ [0,1[

A: Ai = ] -i+1, 1 [  A1 = ] 0, 1 [ A2 = ] -1, 1 [ Thus ∩Ai = ]0, 1[

Q: 1. a) Determine whether binary operation is associative and whether it is commutative or not * is…

A: a) Given, a*b=a-b Now, a*b=a-bb*a=b-a So, a*b≠b*a So, * is not commutative Given, a*b=a-b Now,…

Q: Prove the following for Integers a, b, c, d, and e, ab be bc a | d(e - c)

A:

Q: 3). Let L= {0*1* | n>=0}. Using pumping lemma, what can be said about this language?

A: To apply the pumping lemma to the language , we can demonstrate that this language is not regular.…

Q: Let a = (17 3)(5 49 2) and B = (2 3)(7 4)(5 1 8) be elements of Sao. Then, a²5" is O (1 279 4)(3 5…

A: No answer is given.

Q: Which islare the indeterminate form/s? * 00 а. 000 b. 100 С. d. All of these

A:

Q: Show that [my] is o(ny)

A: In the question, it has to be xy instead of xy. So, we are solving the question by taking xy. To…

Q: Define L:Z → Z and M:Z → Z by the rules L(a) = a², M (a) = a mod 5, V a ɛ Z. Find the values of (a)…

A: Composition of two functions f(x) , g(x)  is defined as : (f∘g)(x)=f(g(x))         If we have to…

Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: Let * be a binary operation on R defined by a*b=a+b+2ab then find the identity element w.r.t. *. O…

A:

Q: Given the set The B= (– 4,7]N ( –1, 10) – {7}· supremum of B is

A: Introduction: In mathematical analysis, the infimum and supremum are concepts that generalize the…

Q: Suppose that lal = 12. The number of distinct left cosets of in is: * %3D 12 O 10 O None of the…

A:

Q: H 6. Prove that the distinct equivalence classes of the relation of congruence modulo n are the sets…

A:

Q: 1 S = 0 1000 100,000 10 € = (†)* (k ≥ 1). " 2n-1 (1) ²¹—¹, ...}, 10

A:

Q: - If n is a positive composite integer, prove that there exist a, b € Zn such that à 0 and 60 but ab…

A:

Q: 4. Let Z5 = {0,1,2,3,4}. 4a) Find the value of x that makes (2+5) X5 4 =_1 in Z5 true. Complete the…

A: Given :  ℤ5 = 0, 1, 2, 3, 4. To find : (i) The value of x in  ℤ5  that satisfies  (2 +5 x) ×5 4 = 1.…

Q: z is a subring of of Q: O True O False

A: Given statement is Z is a subring of Q.  We know that N is a subring of Z, which is a subring of Q,…

Q: Define a * b = ab – 3. Is a binary operation on z?

A:

Q: state whether the following quantified formula is true over the natural numbers n = {0,1,2,...}: ∀x…

A: The given formula over the natural numbers n=0, 1, 2, ...: ∀x∀y∃z x2+y2=5⇒xz<yz. We have to…

Q: Let i be a positive integer and A; =] – i + 1,1 [. Then N, A;= O [0,1[ Ø O 10,1[ O 10,1] None of…

A: Intersection of sets which are forming ascending chain(i.e. A1 contained in A2, A2 contained in A3,…