Construct a binary operation ♦ on {a, b, c} that is commutative

Q: Write a complete residue system modulo 13 consisting only of odd integers.

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Q: If 6 decimal digits only are allowed, then the chopped representation of the number 0.123456789 is…

A: Here the number is given as 0.123456789 We need till 6 decimal places If the 7th decimal place is…

Q: How many binary strings of length 10 are there in which the number of O's in the string is not equal…

A: Solution :-

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: When a message that is communicated via public communication networks is received, it must be…

A: Let A denote that the message is authentic. Let K implies that the correct key is used. P(A) = 0.95,…

Q: Assume that product codes are formed from the letters V, T, X, R, S, and Y, and consist of 6 not…

A: Available letters  : V, T , X , R , S, Y Repetition is allowed

Q: from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing the first four fibonacci numbers (x) that…

A: given the set

Q: The ISBN-10 0-669-03925-4 is the result of a transposition of twoadjacent digits not involving the…

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Q: 7. What is the one’s complement of this string “01010100”?

A: The one's complement of a string is obtained by negating every bit in one's complement. This means 0…

Q: Any two integers are congruent modulo to: not a prime nor composite integer o even integer odd…

A: Let a, b are two integers. Two integers a, b are congruent modulo to n (where n is an integer) if…

Q: [0,1] is not countabe.

A: True statement Detailed explanation :-

Q: A passcode is to be created from 2 letters, 2 digits, and 2 special characters (consisting of ?,!,…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: Assume that product codes are formed from the letters A, B, C, D, and E, and consist of 5 not…

A: Product code is formed by the letters A, B, C, D, and E and consists of 5 not necessarily distinct…

Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: what are the congruence classes in the set of intergers?

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Q: (2). What is the binary representation of the following: (a) (64.37109375) 10.

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

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Q: Assume that product codes are formed from the letters Q, X, W, T, S, Z, and Y, and consist of 6 not…

A: 1) There are total 7 letters, such that, Q, X, W, T, S, Z and Y.

Q: is not a binary operation on Q*. O a. + O b.

A: Let G be a set . A binary operation on G is a relation that assigns each ordered pair of element of…

Q: How many unique codes are possibly formed from two characters, where the first character can be 2 to…

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Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

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Q: Suppose a password for a computer system must have at least 7 but no more than 11 characters where…

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Q: If 8 decimal digits only are allowed, then the chopped representation of the number 0.123456789 is…

A: Here the number is given as 0.123456789 We need till 8 decimal places If the 9th decimal place is…

Q: The binary number (10000001) is equal to gray code Select one: O a. 11111110 O b. 10000011 c.…

A: We need to convert the binary number  (10000001) to gray code. The solution is given below.

Q: Assume a country has 3-digit area codes that all have 0 or 1 as the middle digit, do not have 0 or 1…

A: Solution: From the given information, 3-digit area code should be formed. The first digit do not…

Q: ive an example of a binary operation on Z (integers) that is not commutative

A: Binary operation: A binary operation on a set S is a mapping of the elements of the Cartesian…

Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

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Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

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Q: Show that one of the prime divisors of any three-digit composite number is less than 31 prime, or…

A: A composite integer a has a prime factor p only if p≤a that is if p≥a than there exist another prime…

Q: Assume that product codes are formed from the letters T, Z, Q, V, Y, U, and X, and consist of 6 not…

A: To determine the total number of product codes satisfying different specified conditions

Q: Compute bar 6 - bar 9 in integer Z23

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Q: When a binary operation is performed on two elements in a set and the result is the identity element…

A: When a binary operation is performed on two elements in a set and the result is the identity element…

Q: Is multiplication modulo 6 a binary operation on Z6^*? why or why not?

A: Take two elements in the set.Check whether multiplication modulo 6 of two elements is again in the…

Q: Show that the set {2/3, 1/3, 2/9, 1/6,...} is countable

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Q: Any two integers are congruent modulo to: even integer odd integer Prime integer not a prime nor…

A: suppose n is a positive integer. Then two integers are said to be congruent modulo n if (a-b) is…

Q: Prove that in any set of 700 English words, there must be at least two that begin with the same pair…

A: Prove that in any set of 700 English words, there must be at least two that begin with the same pair…

Q: A five character computer password can be formed from three digits, followed by two lower case…

A: There are totally 26 lower case letters of the alphabets(a-z) and 10 digits (0-9). A five character…

Q: (b) Prove that multiplication mod n is commutative.

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Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

A:

Q: Prove that ADAM - AFAN.

A: Given Also

Q: There are 17 distinct congruence classes modulo 19. True False

A: we know that from the property of congruence classes    There are exactly n distinct congruence…

Q: Determine if the specified operation is a binary operation on the given set.the operation subtract…

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Q: Use the congruence c= (3p + 1) mod 26 to encode the message COLOR MONITOR.

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Q: 2. Suppose that a password for a computer system must have at least 8, but no more than 12,…

A: As Dr. S. N. De said "A permutation of a set is defined as an arrangement of its members into a…

Q: If 8 decimal digits only are allowed, then the chopped representation of the number 0.123456789 is…

A: Rule is that,  if the 9th digit is greater tha 5 the the 8th digit will be add by 1

Q: Show that the principle of mathematical induction implies that I is the leact p natural number.

A: Solution of the problem as follows

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

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Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A: We will use basic combinatorics.

Q: Find a multiplicative inverse of  21 modulo 46

A: