The following is a Cayley table for a group G. The order of 4 is: 1 2 3 4 1 3 4 5 4 4 5 2 4 1 2 3 4 5 3 4 23 HN3 4 4. 3. 1. 2. 3.

Q: Consider the group (Z,*) defined as a*b=a=b , then identity (Neutral) element is

A: Given that ℤ,* is a group. where * is defined as a*b=a=b. That is a-b=0. To find the neutral element…

Q: In the following Cayley table for a group G, C(2)= 1 2 3 5 2 3 5 1 2 3 4 4 3 4 5 4 5 1 3 4 1 2 3 5 O…

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Q: The following is a Cayley table for a group G. 2.5.4 = 2| 1 2 3 4 1 3 4 1 3 4 1 2 3 3 4 1 4 1 2 1 3…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The following is a Cayley table for a group G. The order of 3 is: 1 2 3. 4 2 3. 4 5 1 2 3 4 5 2 3 4…

A: In given Cayley Table :            * 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1…

Q: H and K are subgroup of a group G, then which of the following is a group? a) HUK b) HK c) HnK d)KH.

A: Subgroup: Let (G,*) be a group and H be a non-empty subset of G; then, H is called subgroup if H…

Q: Determine whether the following is a semigroup, monoid, or a group. 1. G=Z, a*b = a + ab 2. G=2Z,…

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Q: The following is a Cayley table for a group G. The order of 4 is: 2 3 5 2 3 4 5 3 4 1 2 4 2 1 3 2 3…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Which of the following is the identity element in the group Z/14Z × µs O (147,0) O (142,1) O…

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Q: Let S9 be the symmetric group and let a be an element of S, defined by: 4 5 6 7 8 9 2 9 867 1 2 3 )…

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Q: Compute the left regular representation of the group G = {e,a, b} given by the group table below by…

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Q: In the following Cayley table for a group G, C(2)= 1 2 2 3 4 5 3 4 5 2 3 4 5 2 3 4 1 2 3 1 2 3 4 5 2…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: In the following Cayley table for a group G, C(3}= 2 3 4 3 4 5 4 1 3 4 1 2 3 2 3 4 4 2 4 O {1,2,4} G…

A: If G be a group and a belongs to G then c(a) = { x : ax = xa , where x belongs in G}.

Q: We will now consider three irreducible representations for the permutation group P(3): E A B I : (1)…

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Q: Let G be a group and a be an element of this group such that a^6=e. The possible orders of a are: *…

A: First option is correct.

Q: If a is an element of order 8 of a group G, and

A: Let G be a group. Let a is an element of order 8 of group G. That is, a8=e          where e is an…

Q: Let G be a group and let H< G. If [G: H] = 16 and |H| = 21, then what is |G|?

A: The expression, G:H can be written as GH .

Q: The following is a Cayley table for a group G. The order of4 is: 2 1 3 3 4 1 4 1 4 1 5. 2 512 m 45…

A: By observing the Cayley table :

Q: Show that each of the following is not a group. 1. * defined on Z by a*b = |a+b|

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Q: Let G be a group and a be an element of this group such that a^6=e. The possible orders of a are: *…

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Q: Consider the group (Z,*) defined as a*b=a+b , then identity (Neutral) element is     a 1   b -1…

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Q: In a group G,let a,b and ab have order 2.show that ab=ba

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Q: The following is a Cayley table for a group G. The order of 3 is: 2 4 2 4 2 3 4 1 3 4 5 2 4 ere to…

A: Given Cayley table

Q: 2. In each case determine whether the two given groups are isomorphic. Justify your answer. a) (2Z,…

A: a) Given that the groups are 2ℤ,+ and 3ℤ,+.The function is given by φ:2ℤ→3ℤ and can be defined as…

Q: 10) Which of the following is a group? * O (Z,*), a* b = a + b - 1 va, b e Z O (Z,*), a* b = a - 2b…

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Q: If a is an element of order 8 of a group G,

A: Let G be a group. Let a be an element of order 8 of group G. That is, a8=e  where e is an identity…

Q: 27. If g and h have orders 15 and 16 respectively in a group G, what is the order of (9) n (h)?

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Q: Let E = Q(√2, √5). What is the order of the group Gal(E/Q)?What is the order of Gal(Q(√10)/Q)?

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Q: The following is a Cayley table for a group G. The order of 4 * 5 is: 1 3 5 2 3 4 5 2 3 4 2 3 4 5 1…

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Q: Consider the group D4

A: Given: Group D4=a,b=e=1,a,a2,a3,b,ab,a2b,a3b and a=1 2 3 4, b= 2, 4 To find : The value of…

Q: In the following Cayley table for a group G, C(3)= 2| 1 3. 4 1| 2 3 4 5 2 3 4 1| 2 3 4 5 1 2 4 5 1 2…

A: The G = {1, 2, 3, 4, 5} 3 * 1 = 4 = 1 *3 3 * 2 = 5 = 2 * 3 3 * 3 = 1 = 3 * 3 3 * 4 = 2 = 4 * 3 3 * 5…

Q: Let G be a group. Let x,y e G be such that O(x) = 4, O(y) = 2, x^3 y = yx. Then O(xy) is 6. Infinity…

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Q: Which of the following is the only trivial sub- group of a group G = {e, a,b, c}? {e,b} {e, a, b, c}…

A: We have to check

Q: 10) Which of the following is not a group? * (Z,*), a* b = a + 2b Va, b E Z O (Z,*), a* b = a +b Va,…

A: Option (1) is correct.

Q: Let G be a group and a be an element of this group such that a^63e. The possible orders of a are: *…

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Q: Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3…

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Q: 6. If G is a group and a is an element of G, show that C(a) = C(a')

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Q: 15.Consider the group (A, *) where *is defined by the table below A B C D ABA D C BA B C D C D C A B…

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Q: Which of the following is the only trivial sub-group of a group G = {e, a, b, c}? {e}, {e, a, b, c},…

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Q: QUESTION 3 Construct the group table for (U(9), ).

A: 3 We have to construct the group table for U9,⋅9. First of all we will write the element of U9,…

Q: In the following Cayley table for a group G, C(2)= 1 2 4 5 3 4 4 2 3 4 2 3 4 1 3 4 2 4 5 {1,2,3,5}…

A: We Know that Let G be a group with operation *. The centre of G, denoted by C(G) is the subset of G…

Q: Let G be a group and a be an element of this group such that a^6=e. The possible orders of a are: O…

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Q: b. For each of the following, show that G is a group using the operation of S4, and determine how…

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Q: The following is a Cayley table for a group G. 2* 5*4 = 1 2 3 5 2 3 4 3 4 2 3 5 1 4 2 3 4 1 2 4 1.…

A: Cayley table for a group G is given as, The objective is to find 2*5*4 Since, G is a group. Hence,…

Q: The following is a Cayley table for a group G. 2* 3 * 4 = 1 2 3 4 5 2 3 4 2 4 1 2 3 4 2 3 4 2 4 1 2…

A: From given table it is clear that

Q: The following is a Cayley table for a group G. 2* 5 * 4 = * 1 2 3 4 5 1 2 3 4 5 2 3 4 5 2 3 4 5 2 4…

A: 1

Q: Let G be a group and a be an element of this group such that a12 = e. The possible orders of a are:…

A: Option (4)

Q: Suppose that N and M are two normal subgroups of a group and that IOM = {e}. Show that for any n E…

A: Given: N and M are two normal subgroups of G and N ∩ M = {e} To prove: nm = mn for any n∈ N and m∈ M

Q: Let a,b be elements of S6 (symmetric group) where a=(1,2)(4,5) and b=(1,6,5,3,2).verify that…

A: Given: Let a,b be elements of S6 (Symmetric group) where a=(1,2)(4,5) and b=(1,6,5,3,2).

Q: (b) Complete the following character table of a group of order 12: 1 3 4 X1 X2 X3 4,

A: The character table of a group of order 12:

Q: G be the external direct product of groups G, G2.. H, = {4,e2.e*, e..e,x, e G,}

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.