1. Consider the group D5. Give five examples of D5 acting on a set, other than the trivial action. For each one, explain clearly what the action is, although you do not need to prove that it is a group action.

Q: Two equalence classes are either disjoint or identically.

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Q: Which of the following are difference sets?

A: Introduction: A (v, k, λ) difference set is a k-element subset D of V = Z (mod v) in which any…

Q: c. How many ways can you choose 3 pieces from the 4 kings and queens (black king, white king, black…

A: Here, order matters. Therefore permutation rule can be applied. Permutation Rule: A permutation is…

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: given n (A⋂B) = 18, n (A) = 3, n (B) and n (A⋂B) = 2.Find n (B) and the number of subsets of set B

A: Solution

Q: Suppose you have the following three sets: A={1,2,3,4,5}, B={3,4,5,6}, and B1={4,5,6}.  If f:A⟶B,…

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Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

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Q: Which of the following sets are closed? Choose ALL that apply. Show the steps. I. The set of…

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Q: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

Q: compos on of mappings is a binary operation by completing the multiplication table for * fi f2 f3 f4…

A: There are four types of basic operations in mathematics (addition , subtraction , multiplication,…

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

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Q: There are lots of ways to split the integers into two sets whose intersection is empty. An example…

A: Let, A= { integers greater than or equal to 0}  and B={ integers less than 0}

Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: Let a, b € N. Choose all correct statements. O gcd(-a, b) = gcd(a, -b) O ged(2a – b, a + b) =…

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Q: How many different 13-letter words (not necessarily mean- ingful) can be made using the letters in…

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Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: What is the domain of the set g= {(2, 1), (3, 5), (4, 7), (5, 9)}

A: GIVEN-  set g is given g={ (2, 1) , (3, 5), (4, 7), (5, 9) }  TO FIND -  DOMAIN OF set g  CONCEPT-…

Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: Let X be a set (P(X),Δ,∩) where  P(X) is the power set of X, and Δ is the symmetric difference. Does…

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Q: 1. Let H = :y and z are real numbers In other words, H is Z the yz-plane in three dimensional space…

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Q: Write the definition of A x B, where A and B are sets A x B = { }.

A: We want to define A x B

Q: d = (a, b, c).

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Q: Consider an interpolating polynomial p(x) of degree ≤ 3 satisfying p(xo) = a, p'(xo) = b, p(x₁) = c…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Show that the following statement is false. If A and B are two sets of positive integers, then…

A: Let A={2,3,4}    B={5,6,7} U={1,2,3,4,5,6,7} Now, A'={ 1,5,6,7}  B' ={1,2,3,4} Now,…

Q: Determine the orders of the elements of D∞

A: It is known that, D∞=a,b|a2=b2=e also it can be observed that, D∞=abka,abk,bak,bakb Let x∈D∞. If…

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: Brenton's weekly pay, P(h), in dollars, is a function of the number of hours he works, h. He gets…

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Q: Consider the following sets: Express each set below using the roster method. Write all elements in…

A: AnswersB ∩ A = {3,5}(B ∩ A) - C = { }=ϕC - (B ∩ A) = {4,6,7}Explanation:(1)B intersection A means…

Q: ould we also use Cantor's diagonalization to contradict this as well?

A: In the question, we have to check that the set of all functions f: N → {0, 1} is countable or…

Q: Consider the set A = {2, 4, 6, 8} with an operation defined by the table. 2 4 6 8 2 8…

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Q: is called the multiplicative identity. • 0 -1 • 9 • 1

A: The multiplicative identity is 1because multiplying a number by 1 leaves it unchanged . If a is any…

Q: Do not Claim ( For all real numbers a, b, c, and do if a = (b +c+d)/3, then either (2b + c) ≤3a, or…

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Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 5…

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Q: Please find all automorphisms. Thanks.

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Q: Let a, b e N. Choose all correct statements. O gcd(a, b) = gcd(-a, -b) O gcd(a, b) = gcd(a², b²) O…

A: We apply property of GCD to solve the problem

Q: Which of the following are difference sets? (ii) {0, 1, 3, 5} in Z13,

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Q: Use the roster method to describe the elements of the following sets. ([-4,6) n (-3, 11)) nZ =…

A: The given sets,The objective is to describe the elements in the given set by roster form.

Q: Suppose a is divisible by b. Show that gcd(a, b) = b.

A: Consider the given information. As we have given that a is divisible by b. then there is a number c…

Q: Σ Find the smallest number n of terms needed to obtain an approximation of the series 10 n = 5 6…

A: The answer provided below has been developed in a clear step by step manner.

Q: 2. Let A and B be finite sets. Prove that A B if and only if |A| = |B|. %3D

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Q: 18. Which of the following functions are NOT differentiable at x =0? Iy=V9-r II. y = x% III. y = x%…

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