The set G: 1,7,43,49,5l,57,93,995 is a gioup unde multipication modulo 100.Determine the isoncrphism Class of this grap.

Q: Find the number of elements in the conjugacy class of (abc)(def) in S₆

A: We have to find the number of elements in the conjugacy class of (a b c)(d e f) in S₆

Q: Let f= (1436578) and g = (1 825 3) (47) be permutations in Sg, written in cycle notation. What is…

A: This is a problem of abstract algebra.

Q: Find the order of U_12

A: We have to find

Q: Find and Explain 5 different examples of application of rings

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Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: exercise 9.5.23) On an 8 × 8 chessboard, a rook is allowed to move any number of squares either…

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Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

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Q: 18. In each part, let T₁: R3-R² be multiplication by A, and let u,= (0, 1, 1) and u₂=(2,-1, 1) and…

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Q: Pzif akb then [a,b]-(- All of a,b are in real numbers

A: The given statements are: p: a<b q: a, b=(-∞, b] \ -∞, a Prove: If p, then q. If a<b, then  a,…

Q: Write a reduced residue system modulo 24

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Q: {(a, b) acb, a and b are finite set of integers}

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Q: Give 3 different examples of norms on Z (set of integers)

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Q: 2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set…

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Q: For the following sets, determine its cardinality.   (ℝ^2)\(ℚ×ℤ)（ is Cartesian product）

A: We find cardinality.     (ℝ^2)\(ℚ×ℤ)（ is Cartesian product）

Q: How would you use the existence and uniqueness theorem here?

A: Here the given initial value problem is,.Existence and Uniqueness theorem :The solution of an…

Q: Q4) Let A = {1,2,3,4} be the given set. Find 1. п(Р(A)) 2. Write power set, P(A) 3. Write a class…

A: Given set is  A={1,2,3,4}

Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: 6. The operation is defined on ordered pairs of integers in the following way: (a, b) (c, d) = b -d…

A: Given: a,b⊗c,d=a-cb-d

Q: Which relations are partial order? O A={5,6,8,10,20} and R={ (a,b) E A x A; a divides b} O Let…

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Q: An operation * is defined on the set R by x * y = x +y+ 6 where x, y are elements of R. What is…

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Q: y QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ X₁ + X2 2) (x1+x²)2 X₁-X2 what dist of 2X² 3) x² + x²

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Q: a set blocks contain blocks of height 1, 2, 4 centimeters. Towers can be contructed by piling some…

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Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

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Q: Z+ as follows: For a, b € Z+, a*b = a - b + 1. Z+? Explain. (3.1) Define an operation * on Is * a…

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Q: Consider the set L:= {(a,b) E Z²| (a – b) is a multiple of 3}. A proposed recursive definition for L…

A: Consider the provided question. L=a,b∈L'a-b is multiple of 3 therefore, a-b=3ka=b+3k  where k is an…

Q: 4. Ax (1-22, 1+22) where A - Z 5. Ax(0, 32, 62) where A - Z 6. A, [5, 10- +] where A = Z' 7. Ax (5+,…

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Q: Define a run in a sequence of symbols.

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Solve the initial value problem. 4 -4 4 y' = 3 -3 - 10 2 15 y, y(0) 1 = 16 14 6

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Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

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Q: the letters in the word COMPUTER be arranged if the

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: Find the cardinality of the set(22,44,88,176)

A: The cardinality of a set is the number of elements  in the set. The given set is 22,44,88,176