Exercise (Check your understanding) 1. Let find A. U = {1,2,3,4,5,6,7,8,9) A = {primes less than 10)

Q: Use the elimination method to find all solutions of the system: x² – 2y = 10 l x² + 5y = 31 The two…

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Q: 3. Given an integer a, then a³ + a² + a is even if and only if a is even. 4. Given an integer a,…

A: As required in the question, detailed proof of 3, 5 and 9 are given as follows :

Q: Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.…

A: Given Produce the least positive number that is divisible 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11.…

Q: "If a and b are positive integers, a divides b and b divides a, then a = b."

A: To Prove: '' If a and b are positive integers, a divides b and b divides a, then a = b''.

Q: 7 and N{B} 3 and N(A U B) = 10, how are If N{A} A and B related?

A: Given: NA=7, NB=3, NA∪B=10 We know that if NA+NB=NA∪B then there is no common element exist in Aand…

Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: case. What is the relationship between the three numbers below? Explain why it is the xyzb xyz0b…

A: We will first write the given numbers in base 10 representation using the concept of radix…

Q: Using the digits 0,1,2,....8,9 determine how many of each type of the three-digit number can be…

A: Given digits 0, 1, 2, ............., 8, 9 Any three digit number with zero at its first place…

Q: If fN is the set of the first 100 positive integers, A is the set of odd numbers between 50 and 90,…

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

Q: 4. Given an integer a, then a² +4a +5 is odd if and only if a is even. 5. An integer a is odd if and…

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Q: (1+ V5 (3 – V5) Without using a calculator, express in the form a+bV5, where a and b are integers.

A: The given expression is: 1+53-5-2 Express in the form a+b5, where a and b are integers. Rewrite the…

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: Prove the statement that "The sum of three consecutive integer numbers is odd if and only if the…

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Q: Show that yn for all n=1, 2₁- ✓

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Q: - Let a, b, n be positive integers. Prove that if a = b (mod n), then (a, n) = (b, n).

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Q: Let Then where a11 = , a31 = , a12 = -1/9 , a32 = 1/9 1 +-679 A = 1 1 A-¹ = , a13 = 0 a11 a12 a13…

A: a11​=11782​ a12​=117−28​ a13​=11763​ a21​=1175​ a22​=117−4​ a23​=117−9​ a31​=117−13​ a32​=11713​…

Q: List all the primes between 20 and 40 in increasing order (in the form 2,3,5,7,9,11). A/

A: I am attaching image so that you understand each and every step.

Q: Question:  a) prove that 100 can not be written as sum of an odd integer and two even integers.…

A: a) To prove that 100 cannot be written as sum of an odd integer and two even integer. Even integer…

Q: Prove the following + if a Ez then 4 is

A: Divisibility is the basis of the theory of numbers. A number is referred to be divisible by another…

Q: Let ß = (1,3,5,7,9,8,6)(2,4,10). What is the smallest positive integern for which ßn = ß-5?

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Q: 2. Factor 10+1 into a product of primes for k = 1,2,3,4,5.

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Q: Show that if 2" – 1 is a prime number, then n is a prime number.

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Q: Find all numbers p such that all six numbers p, p+2, p+6, p+8, p+12 and p+14 are primes.

A: For the given statement

Q: Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest…

A: Given that, A numver is, 2n - 1 Where n = 2, 3, 4, 5, 6, 7, ............ We have to find the…

Q: Discrete Mathematics: Prove that every prime number greater than 3 is either one or more or one less…

A: We need to prove that any prime number which is greater than 3 is either 1 more than or 1 less than…

Q: Show that if a and b are relatively prime then (a+2b,2a+b)=1 or 3.

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Q: If a and b are two integers such that a = bq +r, with b> 0, then %3D gcd(a, b) # gcd(b,r) gcd(a, b)…

A: Let a = bq + r   … (1)Now,  let d1   = gcd ( a,b) then ⇒d1  | a  and   d1  | b ⇒d1 | a - bq   and d1…

Q: Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number?…

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