rove that if x and y are odd positive integers ,then x+y is even but not divisible by 4

Q: 91. Use the Factor Theorem to prove that x - c is a factor of x" – c" for any positive integer n.

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Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b).…

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Q: a|b_ then a|bc for all integers c. ulgn İhi

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Q: onsider (G,*) where * is defined as a*b3Da is the set of all non-zero real numbers

A: Let  G=ℝ-0For a,b∈G⇒a*b=ab2a,b∈ℝ-0⇒ab2∈ℝ-0a*b∈G   The closure prosperity For…

Q: a|b then albc for all integers c.

A: From the question, a|b means that a divides b, and similarly, a|bc means that a divides bc. We need…

Q: 6. Let r> 2 be an integer. Show that R(2r, 2r) > 2

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Q: a|b then albc for all integers с.

A: Statement is ture

Q: (a) Prove that (-1+iv3)" + (-1– iv3)" has either the value 2"+1 or the value –2" if n is any integer…

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Q: Suppose x and y are integers. Show that If x y, then x | 3y - y + 5y. 1) What is your assumption? 2)…

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Q: Z+ is the set of positive integers. Let A = {1,2,3), B = {n ∈ Z+ | n is even}, C = {n ∈ Z+ | n is…

A: concept Used: C∩D is the set  containing all elements of C that also in the set D C∪D is the set…

Q: Discrete mathematics: Prove that if a is an integer other than 0, then a divides 0.

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Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: b) Prove by contradiction: There exist three consecutive odd integer a, b, and c such that a? + b² =…

A: Explanation: Given that,  3 consecutive odd integers a, b & c. Let us assume m & n are…

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: Use two column proof and state reasons. Let x be the product of 5 distinct integers, where each of…

A: Given: Let x be the product of five unique integers, each of which is in the range of 1 to 63,…

Q: Prove or Disprove: If x is an integer and 7x³+9 is even, then x is odd.

A: According to the given information, it is required to prove or disprove the given statement.

Q: Using formal logic prove that for each integer a, if a -1 is even, then 4 divides a-1 by…

A: We have to prove that the proposition "If a2-1 is even, then 4 divides a2-1" using formal logic. We…

Q: Show that if a and b are coprime integers, then gcd(a + b, a² – ab + b²) = 1 or 3.

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Q: ive integers such that gcd (a, a² b²) = 1. T

A: Given as, gcda,a2-b2=1

Q: R.2. Let S represent the set of positive integers that are perfect squares, and let C represent the…

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Q: 4. Prove or Disprove Prove or disprove that for all real numbers a and b, if a? = b² then a = b. %3D

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Q: (a) Given A = use the Cayley-Hamilton theorem to find (1) A¹-3A6+ A¹+3A³-2A²+31 (ii) A¹, where k> 0…

A: (a) Given A=2011 To use the Cayley-Hamilton theorem to find (i). A7-3A6+A4+3A3-2A2+3I (ii) Ak, where…

Q: 4. Prove that (a + b) ≤a+b≤ a + b for any real numbers a and b. (Hint: Use cases when a, b ≥ 0; a, b…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let a and b two positive integers. Then we have that axb LCM(a,b) = GCD(a,b). O True O False

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Q: Using Contrapositive Prove that for any integer a, the integer a(a+1) is even

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Q: Find all positive integers a, b such that a | b^2-b+1 and b | a^2-a+1

A: Solution :-

Q: Discrete Math Use a direct proof to prove the following: If x, y, and z are integers and xy|z, then…

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Q: Let a, b, c be distinct positive real numbers and nbe a natural number. If a, b, c are either in…

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Q: (a) Use proof by contradiction to show that there is no positive real number r such that x-2 X > X…

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Q: 4. Prove or Disprove Prove or disprove that for all real numbers a and b, if a² = b² then a = b.

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Q: Prove using Direct Proof: For all integers a,b and c if a|b and b|c then a|c

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Q: L) Prove that (3-2)(x+2) = 3 +21 iFitwas

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Q: DISCRETE MATH use ANY METHOD of proof. 1. Prove that if a and b are positive integers such that a|b…

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Q: a) Prove that the sum of the squares of two odd integers is always even.

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Q: square of any odd integer is od.

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Q: Prove or disprove: If a and b are odd integers, then 4 | (a – b) or 4 | (a+b). -

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Q: Using indirect proof, prove:  Let a, b, and c be integers. Prove that if a divides b and a divides…

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Q: true of false:   (v) Given an integer n ≥ 2, [a]n ×n [0]n = [a]n for any integer a.

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Q: Prove that there do not exist positive integers a and n such that a? + 3 = 3".

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Q: 2. Show that if a and b are positive integers and alb, then a < b. 3. Show that if a and b are…

A: Basic facts about division will be used in solving this problem.

Q: . Show that there exist no nonzero real numbers a and b such that va² + b? = Va³+b.

A: To remove the radical sign in the equation a2+b2=a3+b33, raise the power to 6 on both sides of the…

Q: 1.Prove that the product of two consecutive integers is divisible by 2.                   (Use…

A: Product of two consecutive integers is divisible by 2

Q: Using direct, indirect and contradiction 1. Prove that if n is a positive integer, then n is odd if…

A: To Prove that if n is a positive integer, then n is odd if and only if 5n + 6 is odd.

Q: The QRT states that for any integers n and d (d non-zero), we can find unique integers q and r such…

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Q: Prove or disprove:  For all integers a and b, if a+b is even, then a is even and b is even.

A: We disprove this statement by taking a counter example.

Q: Using the direct proof method, prove that for every integer a, if (a-2) is divisible by 3, then…

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Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4. 1 0 01 0 0 0…

A: As per our guides lines I answered only 1st part

Q: True or False: For all integers a, b, and c, if a divides b and b divides c, then a divides c. True…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.