An onto grouphomomorphisimf: G H is an isomorpisim if and only if Select one: a. f(1,)=H b. f(16)=f(1,) c. ker(f)= 1, d. ker(f)= 16

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To  write down the table for the fuzzy composite relation

Q: 2.47. Let P(x) be the assertion "x is odd", and let Q(x) be the assertion "x2 - 1 is divisible by…

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

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: Prove that G1 ⨁ G2 is isomorphic to G2 ⨁ G1. State the general case

A: To Prove: G1⊕G2 is isomorphic to G2⊕G1. Also, state the general case.

Q: Determine all homomorphisms from ZO Z2 to S3.

A: Z×Z2→S3Z has subgroups like  mZ   where m∈ZZ2 has subgroups 0,Z2now apply fundamental theorem of…

Q: T -2 4 f(x) g(r)|h(r) 5 4 9 2 -3

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: 15- R {(x,y) EZ XZI(y-x) = even element} is an symmetric %3D 16- R {(x,y) EZXZI(y-x) = even element}…

A: Recall: Reflexive, symmetry and Transitivity:   Let R be a binary relation on a set A. R is…

Q: Q3. Write the Disjunctive normal form of Boolean Polynomial p = x (y+z)' + ( x y + z ) x'.

A: Disjunctive Normal form: A Boolean expression is said to be disjunctive normal form (DNF) if it is…

Q: Let A = [-1,2,-3,4; 0,a,b,c; 0,0,-1,0;0,0,0,d]. Determine det(A) in terms of the unknown constants…

A: The given matrix is

Q: 3. Let R-Z18. Determine the units and zero divisors of R giving the explicit unit or zero divisor…

A: We know that  no of units in ring Zn = phi(n), and  no of zero divisor of Zn = n - phi(n) -1

Q: Draw the subfield lattices of GF(318) and of GF(230).

A: To draw the subfield lattices of  GF318 and GF230.

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: Let T: R² R² be given by T(x1, x₂) = -[at] It is known that I is an isomorphism. T-¹ is given by the…

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Q: Limikadity malfing ASomozphic Oxdexed sets:-

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Q: {(a,b, c)/b=a+c} defined on Z×Z×Z,where Z be the set (d) List five elements of the ternary relation…

A: Note:  For (d), We need to list five elements of the ternary relation S = {(a, b, c)| b = a+c}…

Q: a b 2.3 Let e: (M,(R), +) → be defined by e a + d. where a,b,c,d ER (a) Prove that e is a…

A: Given that θ:M2ℝ,+→ℝ,+ is a mapping defined by θabcd=a+d where a, b, c, d∈ℝ. We have to prove that θ…

Q: Find a rule for the following isomorphism: 9: Z2 x Z3 + Zz x Z2 p (a, b) = (

A: we have φ:z2×z3→z3×z2 we know a result: A G1⊕G2 is isomorphic to G2⊕G1 by g1,g2→g2,g1.

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

A:

Q: Define complemented lattice. Let (L, *,Ð, ', 0,1) be a Boolean algebra. Then show the following:…

A: Given: (L,*,⊕,',0,1) is a Boolean algebra.We need to define complemented lattice and show that…

Q: Let T={[a, ) : a€R}, then T is not Borel algebra.

A:

Q: If G,=(-,1), then {G„}n€Nis a countable open cover of (0,1) .A O (a cover of [0,1.B O not an open…

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Q: 2.3 Let 9: (M2(R), +)→ be defined by e c d a b = a +d. where a,b,c,d €R (a) Prove that e is a…

A: A mapping f:(G,+)→(H,+) is said to be group homomorphism if it satisfies: f(a+b)=f(a)+f(b)…

Q: Let G = Z5OU(7). The identity of G is O (0, 1) O (1, 1) O None of the choices O (1, 0) O (0, 0)

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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…

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Q: is the columd of matnla A Explain why Oineanly nメn an A is invertible. independent when are 1 6

A: To explain why the columns of an n x n matrix A are linearly independent when A is invertible.

Q: Let E-f(): 05 05 n. 05 25 1.7√/25 rs 7). Compute 6.8365-1051090 11²³ dv

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Q: If B is a proper subset of A, then which of the following must be true? Select all that apply: 03x(x…

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Q: 4. Let X1, ,X4 be iid Unif(0, 0). (a) Show that X(4) is independent of X(1)/X(4). (b) Show that X(4)…

A: Given that X1,X2.............,X4 be iid Unif0,θ (a) X4 is complete sufficient statistics and…

Q: b) For 7 in R", we say that is in the kernel of T if T(x) = 0. If x₁ and 2 are both in the kernel of…

A:

Q: Task 1.5 For let a,b E Z = Z \ {0} ' GCD (a,b) denote the greatest common divisor of a and b. The…

A: COMMUTATIVE PROPERTY Consider the values, a=8b=12 Consider the following, GCD8,12=4GCD12,8=4 Since…

Q: Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A−¹,…

A:

Q: 1. Consider permutations a = 2 3 4 5 6 6 4 51 2 2 3 4 2 4 6 5 3 6. in Sg. and r = Find: (a)…

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