is an element in X that is not in Y. O No element in Y is in X. O There is an element in Y that is not in X. O No element in X is in Y. Let A = {n EZn = 5r for some integer r} and B = {m eZ| m= 20s for some integer s). Determine which of the following statements are true and which are f statement is true, and enter a number that could be used as the basis for a counterexample if the statement is false). (a) ACB= (b) BCA =

Q: Let x and y be positive integers such that the prime factorization of x has exactly four 5’s and…

A: We have to find how many 5’s does the prime factorization of x + y contain.

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Q: 2. Prove by mathematical induCHon that १) के) 22 32 42 2n is Hrue For all integers nz 2

A:

Q: 30. If S is the set of negative integers sup S does not exists sup S = 0 sup S is any nonnegative…

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: show that for eury A s integer nz3; A n- Am-2 +A2J. Mence determine ASO.

A: To show: That An=An-2+A2-I for n≥3 then find A50. Given: The matrix is A=100101010. Calculation:…

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Q: For each statement below decide if it is TRUE or FALSE. • There are two integers n and m such that…

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Q: Suppose n₁, n₂ are positive integers and gcd(01, n₂) = 1. Then for every integer x, if n₁x and n₂|x,…

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Q: Prove by contraposition: For all positive integers n, r and s, if rs ≤ n, then r ≤√n or s ≤√n

A: Consider the statements p and q as-                 p : For all positive integers n, r and s,   rs ≤…

Q: If In x + In(x – 7) = In(2x), then x =

A: Given that ln x+ ln(x-7)=ln(2x)

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A:

Q: If k = (0.0003,-0.0012,0.0015,-0.0014)' in R then -5.2| |L = Select one: True False

A: Given  k = 0.0003, -0.0012, 0.0015, -0.0014t in R4.

Q: Suppose if p and q are odd integers with p!= q (p is not equal to q). Show that there is a unique…

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Q: 3. Show that if a and b are integers such that alb, then ak|b* for every positive integer k.

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Q: Prove by Contradiction: There are no integers x and y such that = 4y+2.

A: We have to prove the statement "There are no integers x and y such that x2=4y+2" by contradiction.…

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

A:

Q: Prove that 36n is not O(35n)

A: Let, 36n∈O35n

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Q: prove that it ņ is an 3n +2 is odd then integer and is add

A: This is related to Number System

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A: Given that for positive integers a,b,c,d,e,f , d=gcda,b,ce=gcda,bf=gcde,c

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A: We have to check

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Q: prove by contrapositive : for all n,m integers if nm is even then n is even or m is even

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Q: Prove that 3|(52n – 1) for all ne N.

A: We prove it by mathematical induction. 1st step We show that the statement is true for n = 1.…

Q: (1) Disprove the statement "For all integers a, b if a | b2 and a < b then a | b." by giving a…

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Q: Determine whether 5 and 7 are irreducible or not in Zi. O 5 is reducible but 7 is irreducible. O 5…

A: Here , both 5 and 7 are irreducible because both cannot be reduced further. As both are neither in…

Q: Let m, n, p be integers. Use direct proof to show that if m+n and n+p are odd then m+p is even.

A:

Q: For any positive integer n and r = 1,2, ...,n, we have G) = (","') + C" - }). True O False

A: The expression nr can be presented in the factorial form as follows. nr=n!(n-r)!r! The expression…

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Q: Suppose j and n are postive integers with n-j n > j, then ak = E -Σ ak+j k=j k=0 17 Select one: O…

A: In this question we have to express that both sides are equal.

Q: Prove the following using the appropriate method.    Let a, b be integers. If ab is even, then at…

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Q: Let n and r be non-negative integers such that r <n. Then, C + "C , = **C,

A: nCr=n!r!(n-r)!

Q: Establish that if a is an odd integer, then 2" = 1 (mod 2" +2) for any n 2 1.

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Q: Let a and b be integers, not both zero. Then a and b are relativelyprimeif and only if 1 = ax + by,…

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Q: a) Any integer with factorisation 39.76.11€ where a, b, c € N, is said to be 9-regular if and only…

A: Please see the below picture for detailed solution.

Q: Let S be the set of positive integers less than 500. Find the number of integers in S that are…

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Q: Let a and b be integers, not both zero. Then a and b are relativelyprimeif and only if a)1 = ax +…

A: Option D will be the right answer.