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

Q: 1. Let A = {1, 3, 12, 35}, B = {3, 7, 12, 20), and C = {x | x is a prime number}. List the elements…

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Q: True or False: Given set A, if B is an element of P(A), then BC A

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Q: Prove the following statement: For all integers x and y, if x and y are even, then 3x + 5y is even

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Q: Is (R,#) a poset? If it is a poset, is it a total order? (R is the set of all real numbers)

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Q: A ∪ B ∪ C={1,2,3,4,5} and  A ∩ B ∩  C={}.

A: A,B,C  are sets that  A∪B∪C={1,2,3,4,5} and A∩B∩C={}

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to determine whether the set {3, 7} is a subset of the set A = {2,…

Q: The rules of mathematical logic specify methods of reasoning mathematical statements. These rules…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: "For integers a and b, if both a and b are odd, then a² + ab + 5b is odd as well

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Q: If  n(A) = 106, n(A ∪ B) = 152, and n(A ∩ B) = 48, find n(B).

A: Introduction: We carry out specific operations in mathematics, such as addition, subtraction,…

Q: prove the following statement. let a,b, and c  be three counting numbers. then, gcd(ac,bc)=c…

A: To prove the statement gcd(ac,bc)=c gcd(a,b), use the following two properties of the greatest…

Q: Place the polar coordinates of each point of the figure in the table. Show your solutions in every…

A: As per the question we are given a figure on the polar (r, θ) plane consisting of five points. And…

Q: Suppose A, B, C are integers. Prove that if AB + BC+CA is odd, then at least two out of A, B, C are…

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Q: 2. If a set X has n elements, how many elements are in the power set P(X), we exclude the empty set…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 5. If A is a set with 5 elements, how many elements are in P(A), the power set of A.

A: The given problem is to find that how many elements are there in power set of A, P(A) Given A is the…

Q: Evaluate Σ 71-0 1 (2+i)

A: The given series ∑n=0∞12+in We have to find the sum of the series.

Q: ZFC How does the Axiom of Separation prevent Russell's paradox? Thanks

A: The Axiom of Separation, also known as the Axiom of Subset Selection or the Axiom of Comprehension,…

Q: Give a combinatorial proof the following statement 1(n−0) + 2(n−1) + 3(n−2) + 4(n−3) +···+ (n−1)2 +…

A: To give a combinatorial proof for an identity, we do the following steps Find a counting problem…

Q: 3) Determine if the proposition "Every set is an element of its power set" is true or false, and…

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Q: 3. Every nonzero rational number can be written as the product of three irrational numbers. For…

A: As per our guideline i am solving only no. 3. For no. 4 kindly resubmit the question mentioning…

Q: 10 Different People order 3 donuts each, chosen from 5 types of donuts. At least one person chooses…

A: (a) Thee will be 10 different possibilities for number of person to pick all 3 donuts of the first…

Q: Which among the following statements is (are) true? O There is a finite set with exactly 90 subsets…

A: In general, if you have n elements in your set, then there are exactly 2n subsets and         (2n −…

Q: Determine which pairs of actions are commutative.  “taking a test” and “studying for the test”

A: To determine Which pairs of actions are commutative.   “taking a test” and “studying for the test”

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: SEt!bこN

A: Given vector, v→=4i+3j

Q: definition (using logical symbols-state what the variables are): (a) Odd integer; (b) perfect…

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Q: 3. Prove the following statement using a proof by cases. Explicitly indicate all possible cases and…

A: Remark: Product of an even integer with any even or integer must be even. Also product of two odd…

Q: A = all whole numbers except 12 B = all whole numbers except 17 C= {5, 6, 7, 8, 9, ..} %3D a. Is A…

A: Given

Q: The notions of decidability and effective enumerability are applicable not only to sets of…

A: To prove the statement, we need to show both directions of the "if and only if" statement: 1. If set…

Q: Given the sets Determine which one is a subset of the other. Prove that subset property by universal…

A: To determine which set is a subset of the other, we can try to find a counter-example where an…

Q: are true regarding permutation and combination? See image below for the statements. 1 - Permutation…

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Q: IV. Two integers x and y are said to be of the same parity if x and y are both even or are both odd.…

A: We shall be using basic divisiblity criterion for solving this problem.

Q: 2- Two sets P &Q are said to be Equal

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: I. Prove the following assertions using a direct proof. a. If x is an odd integer, then x+5 is even.…

A: According to guidelines we can solve only 3 subpart.

Q: Listed below are six eight-letter words. Rank the words in order of the number of unique ways to…

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Q: or all integers x and y, if x is even, then ry is ever

A: For all integers x and y, if x is even then xy is even. Remember : An even integer is a multiple of…

Q: For each of the following concepts encountered during the course, give the precise definition (using…

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Q: states that begin with the letter B is null, finite, or infinite

A: I have provided solution in step2.

Q: Prove the following statement: There exists a whole number m such that m² - m - 12 = 0

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Q: (DO NOT use any other symbol except numbers in the answer slot ) Three Baltic countries(Lithuania,…

A: It is given that there are 11 countries separated as 3 groups as Baltic countries (Lithuania,…