from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing the first four fibonacci numbers (x) that are congruent to 0 modulo 3

Q: How many unique codes are possibly formed from three parts, where the first part can be A to E, the…

A:

Q: Any two integers are congruent modulo .. when they are both even or both odd. greatest common…

A: Greatest common divisor

Q: 2) Each type of machine part made in a factory is stamped with a code of the form…

A: We can use :- 26 letters, 10 digits, 10 digits (as digits can be repeated)   Total number of…

Q: Which numbers from the set{-63,-54, -41, 11, 13, 76, 80, 130, 132, 137} are congruent to 7 mod 13?…

A:

Q: list five different natural numbers that are congruent to 10 modulo 4

A: We know that a≡b(mod m) if m  divides a-b 14≡10 (mod 4)  ∵ 14-10 =4 which divides 4 18≡10 (mod 4)  ∵…

Q: Any two integers are congruent modulo .when they are both even or both odd. Least common multiple…

A: Answer : smallest prime n=2

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: How many four digit positive integers are there that contain the digit 3 and are divisible by 5?

A: A number is divisible by 5, if the unit digit place contains the number 0 or 5. Let m choices to be…

Q: The set {1,2,3,4} under multiplication modulo 5.

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Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

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Q: The set of elements in (-, 9) or (-, 12) or in both sets is .

A: The sets are (-∞,9) , (-∞,12)

Q: from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing first five prime numbers (x) greater than 50…

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Q: Give three elements of the equivalence class of 15 modulo 7

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Q: How many different passwords exist that consist of 12 characte using uppercase and lowercase…

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Q: The set {0,5,6} is closed under Mod(10)

A: To check if { 0 5, 6} is closed under mod(10)

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: modulo 5   B).  Evaluate 31mod5

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Q: How many integers have inverses modulo 144? Justify.

A: Justify how many integers have inverse modulo 144.

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: Create your own symbols for the digits 0, 1, 2, 3, 4, 5, 6, 7,8 and 9. Explain the relevance of each…

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Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: Number theory

A:

Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: Which numbers from the set{-63, -54, -41, 11, 13, 76, 80, 130, 132, 137} are congruent to 7 mod 13?…

A:

Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

Q: How many strings of eight uppercase English letters are there that start with X, if no letters are…

A: We have 26 possible letters in English alphabet: Now we have to form a string of eight uppercase…

Q: List six intergers that are congruent to 7 modulo 9.

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Q: Evaluate: mod 13= -19 div 7

A: To find: 98 mod 13

Q: determine what number the sum is congruent to in mod 3, 6+4 = __ (mod 3)

A: First we add the numbers, then check for the remainder on dividing the result by 3 and that will be…

Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8, 9​}…

A: given:  set ​{1, 2, 3, 4, 5, 6, 7, 8, 9​}   if no element may be used more than once in a number and…

Q: Any two integers are congruent modulo . when they are both even or both odd. greatest common divisor…

A: Any two integers are congruent modulo... when they are both even or both odd.

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

A:

Q: Prove (1.2), (1.3), and (1.4).  

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

A:

Q: Use Chinese theorem to find all positive integers that makes this congruence true:        x = 2 mod…

A:

Q: Create your own symbols for the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Explain the relevance of…

A: The question asks to create new symbols for the digits 0 to 9. The digits themselves are symbols, so…

Q: How many 4-digit codes can be formed from the digits 1,3,5,7, and 9 if repetition of digits is not…

A:

Q: Prove that every third Fibonacci number in 0, 1, 1, 2, 3, ... is even.

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Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: How many strings of eight uppercase English letters are there that start and end with X, if letters…

A: In English Alphabet we have 26 letters. We have to make a string of 8 uppercase English Letters.…

Q: Determine whether 17 is congruent to 5 modulo 6?

A: We have to check whether 17 is congruent to 5 modulo 6

Q: Find the order of 5 modulo 31.

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Q: Consider 4 digit numbers with each digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} .  How many such…

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Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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Q: Which numbers from the set {-57, 17, 108, 0, -110, -93, 1111, 130, 232} are congruent to 6 mod 11? O…

A: