sider the Set Q of rational numbers, and let =a+b-ab. Then (Q,*) is a ect one: a. semigroup b. none of these c. group d. subgroup

Q: Could you please help me out with this problem? Is asking to classify all elements of R/∼….

A: Classification of elements in R/∼ :The relation ~ on R is defined as x∼y if and only if (iff) x - y…

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 a, b and c be integers. (i) If cla and alb then cb. (iv) If cla and cļb then c(sa +tb) for all…

A:

Q: Determine which of the options below appropriately demonstrates that Q is not closed under the…

A: Consider the given information: Here to demonstrates that ℚc is not not closed under the operation…

Q: For any nonzero integers a, b, c, k. One of the following statements is true O A. If alb, then |a| <…

A:

Q: Let the operations * and e be defined on the set of integers. Find each of the following are…

A:

Q: 16-(4+r) lim is O a. -8 O b. 8 C. 0 O d.4 O O O

A: This is a limit based question

Q: 5. Show that 2 32 3" 31 3" for all positive integers n.

A:

Q: If A = {x | x is an odd integer}, B= {x|x is an even integer}, C = {2, 3, 4, 5}, and D = {13, 14,…

A:

Q: 5. Let r,ne N. Show that the product (n+1)(n+2)...(n+r) of r consecutive positive integers is…

A:

Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: For all intergers a,if 6|5a,then6|a. Prove or disprove this statement."|"means divides

A:

Q: Let A be the set of odd integers, and let B be the set of positive integers less than 10. Find An B…

A:

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: b. How many elements are in the set {a, {a, b}, {a} }? C. For each positive integer x, let A1` =…

A: Use the definition of set and its elements to solve this problem as in next step.

Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

A:

Q: Determine whether each statement below is true forn = 1, 2, and 3. Enter a comma-separated list of…

A:

Q: If A is a perfect subset of B and P(a > Pb), then P(A - B) is equal to O a. O b. O c. O d. P(a) /…

A: To determine the value of p(A-B) where A is a perfect subset of B.

Q: How many elements are there in the greatest conjugacy class of 5 ?S

A:

Q: How many integers in the set {1,2, ..., 10°} are divisible by 495 and not by 75?

A:

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

A:

Q: A = {1, 2, 3} b. A = {0, 1, 2, 3} c. A = {-2, -1, 0, 1, 2, 3, …} d. A = {…, - 2, -1, 0, 1, 2, 3}

A:

Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

Q: List all integer elements of B = {19, V6,-13,0,²,7.1, v4 }. 9.

A: Given set is B=19,6,-13,0,59,7.1,4. We know that integers are the elements belonging to the set…

Q: et ZZ be the set of all integers. Let R = {(a, b): a + b is divisible by 3}. a. Show that R is not…

A:

Q: For each pair of integers r and s below, Find the greatest common divisor d. Then, find m, n, such…

A: To determine the greatest common divisor, d and then to find m and n such that d = mr + ns. (a) r=32…

Q: Draw all distinct 4-animals composed of equilateral triangles, squares or regular hexagons that have…

A: The objective is to find all four animals from the given graph.

Q: which of the following defines the positive integers divisible by both 3 and 4? Select one: O a. 12…

A: Explanation of the solution is given below...

Q: For all integers a, b, and c, if a | b and a | c then a (b -c).

A:

Q: a) For all integers a, b, c, d, determine whether each of the following is TRUE or FALSE, Justify…

A:

Q: For any integers, a, b, c, show that if a|b and a|c, then a|(k1b+k2c) for any k1, k2∈Z.

A: Division Algorithm: Let x and y be two integers with y&gt;0.  Then there exist unique integer q and…

Q: For the polynemial 8yt-3y?+| 1. isita monomia, binenial, or trinaMia l? 2. what is its deguee s

A: Given polynomial is In the given polynomial, we have three terms If a polynomial has 3 terms then…