Which of the following is a false statement? OnC, = r!, Pr r!n Pr a combination is an arrangement of objects when order is not important OnCn = 1 where n is any positive integer On Pr=r!n C,

Q: The number of units in Z23[x] is O None 30 28 22

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Q: Prove using the properties of set operations: a. A - B and An B are disjoint.

A: Solution-: We want to prove A-B and A∩B are disjoint.

Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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Q: Simplify the following Boolean Expression using Boolean theorems. F (A, B, C, D) = ABC + ĀD + BD +…

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Q: Express the set in roster form. The set of natural numbers between 14 and 182

A: the set of natural numbers between 14 and 182

Q: Prove using the properties of set operations: a. If A and B are sets then [(A - B)c n A] C B

A: The given expression is A-BC∩A⊂B, where A and B are sets.

Q: (d) D= {n €Z:n −3} (e) E = {}\{}

A: Here we have to find the set D and E in list form.

Q: Which of the following is true? Check all that applies. о (2,7, —1) + (5, -3,4) 3D (2 + 5,7 - 3, —1+…

A: .

Q: You have 14 presents to give to your 3 kids. How many ways can this be done if: a. The presents are…

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Q: Which of the following statements is correct about the set -3 6 -898) 2 -4 -2 S = Select one: O O O…

A: There is set S given. One has to check whether S spans the vector 333 and vector space R3 or not.…

Q: Given A = [2 4] and B = [3; 2], which one of ?the following expressions is illegal A. *BO A+B'A+B' O…

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Q: Cosets

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Q: Assume a, b ER. a+b, a² + b², a³ + b³, and a + b for all integers. Prove that am + bm is an integer…

A: Let us assume that a,b∈ℝ where ℝ is the set of real numbers. It  follows that a,b∈ℤ where ℤ is the…

Q: QU{{-1,0,9,11,17} × {–T, 1}) is an empty set an uncountable set a countable set

A: Given: Set ℚ ∪-1, 0, 9, 11, 17×-π, π

Q: In how many ways can we compose a word of 3 letters from the set {X, Y, Z, F, S} if repetition is…

A: Given, Letter set  = {X, Y, Z, F, S}  words should be 3 letters,

Q: Which of the following sets are countable? Mark all that apply. NXN N OR Z

A: From the given options ℕ×ℕ, ℕ, ℤ and ℚ are countable.

Q: If n is any integer then n and n5 will have? (mcq) A. Both are divisible by 5 B. 10s place is…

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Q: Help with this one please

A: Let's find six members of the set S.As 0∈S so 0+3∈S and 0−3∈S.So we got 3∈S and −3∈S.As 3∈Sso 3+3∈S.…

Q: Let A = and B = is the Sum of the entires What Nrrt it Jt Jton

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Q: A supplier of ballpoint pens guarantees a low defective rate.  Sara receives a shipment of 400 pens…

A: Ww hvae to find values of x ..

Q: Why is the following false? The set (1, 5.2) X [2, 3.14) is open in R X R.

A: Given  S=1,5.2×[2,3.14) in R2 A set is said to be open set if it can be written as finite union of…

Q: The functions fa)= X29 and go)=x-3 X+3 ge the sGme True O False K Quest

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Q: Proposition. For all a, ne Z with n> 2, if a =4n 3n, then a =, 0.

A: To prove - For all a, n ∈ ℤ with n ≥ 2, if a ≡4n 3n, then a ≡n 0

Q: is equivalent to 125 20 O True

A: Here we have to determine the true statement:  254 is equivalent to 12520.

Q: If geRfasbland if how=go) except finlite for of number of number Point infasb) then prove hERfabland…

A: We have to break the integral into subsequent sets.

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Which elements are in the set X = {u E Z |u s 4 or u 2 1}? Select one: a. {1,4} b. {2, 3} c. {1, 2,…

A: Given below the detailed solution

Q: ?Which of the following is a true statement (15 * 2 > 30) AND (15-230) O non of the given (15 * 2…

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Q: Which of the following is an example of an empty set? O {x: x€N,4 sx s 5} O The set of odd natural…

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Q: Let a, be the set {0, 2, 12} Let a, be the set {4,5, 10} Let az be the set {6,9, 14} Let az be the…

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Q: Match operations on sets with their definitions. ✓ AnB AUB A-B - A A. U-A B. {x/x EA V x € B} C.…

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Q: S=(n is an integer and 0 ≤ n ≤ 9), L = (2,3,7,9), M = (2,4,7,8), and N = (0,2,5,8,9).Find the set (L…

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