3. Let x/y= xy + x+ y be a binary operation in the set of integers. a. What is 4/-2? b. Is x/y commutative? C. Is x/y associative?

Q: If the binary operation * is defined on a set of ordered pairs of real number as (a,b)*(c,d)=…

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Q: 11. Prove that for each integer a, if a² – 1 is even, then 4 divides a² – 1.

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Q: prove the following statement: Let n be an integer. If a and b are integers such that a is divisible…

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Q: is not a binary operation on Q*. a. + O b. - O c. * O d. None of them O e. /

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Q: 7. Consider the following table that displays the binary operation on the set (x, y, z). *…

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Q: Which of the following is a binary operation if a and b are in S? a.a*b = ab+ b², S= set of negative…

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Q: Suppose a, b, and c are integers and suppose a | b and a{c, where a}c denotes that c is not…

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Q: Is a * b a +b+3 associative under the binary operation? a. Yes b. No c. Maybe d. Cannot be…

A: The solution is given as

Q: e the binary operation on Z (set of integers) defined by a * b = 2ab +5 ow that + is commutative.…

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Q: a

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Q: Let * be a binary operation on Z defined by a*b = a +b-4 for all a , beZ. Which of the following is…

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

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Q: Prove that if for some integers a, b, c we have that a° + 6° + c° is divisible by 9, thên at least…

A: Here we have to prove that if for some integers a,b,c we have that a3+b3+c3 is divisible by 9,then…

Q: 11. Use set identities or different proof method to show that: a) (B- A)U(C- A) = (BUC)- A b) (4 –…

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Q: (S, *) is said to be algebraic binary structure if (A) * is binary operation on S (B) * is…

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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: Is a *b a+2b - 3 commutative under the binary operation? a. Yes b. No Maybe d. Cannot be determined…

A: We need to check whether the binary operation defined by a*b = a + 2b -3 is commutative.

Q: [0,1] is not countabe. صواب İhi O

A: True

Q: 4. Is the binary operation # defined on the set of real numbers commutative if a#b = a+ 2b + 4, Va,…

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Q: (S, *) is said to be algebraic binary structure if (A) * is binary operation on S (B) * is…

A:

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + n², express an in terms of n.

A: In this question, we solve the recurrence relation  in terms of n an=2an-1+an-2+n2witha1=3a2=4

Q: 4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

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Q: Prove by contraposition: if a, b and e are integers and be is not divisible by a, then b is not…

A: Given a,b and c are integers. Statement : P: bc is not divisible by a. Statement: Q: b is not…

Q: Suppose that a, b, and c are integers. Prove that if a2 +b2 =c2 then a or b is even.

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Q: A binary operation * on a set of integers is defined as x*y = x^2 + y^2. Which one of the following…

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Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: Let x / y= xy + x+ y be a binary operation in the set of integers. Is x / y associative

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Q: 7. Consider the following table that displays the binary operation on the set {x,y,z). I N 8 (a)…

A: This is a question from abstract algebra.

Q: Let the binary operation *, be defined as a * b = a + 2b, where a and b are real numbers. a. What is…

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Q: If a is transcedental over Q then a^2 is also transcedental over Q

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Q: is not a binary operation on Q*. a. + O b. - O C. * O d. None of them O e. /

A: To solve this problem, we use the standered defination of binary operation.

Q: 2. The binary operation * defined on Z by x * y = 1 + x + y on the set of real numbers. Show that *…

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Q: Let x / y= xy + x+ y be a binary operation in the set of integers. What is 4 / - 2 ?

A: Given x/y=xy+x+y  With respect to the above binary operation, we have to find 4/-2

Q: prove that Every positive integer n can be written as n =( 2^a)(5^b)c, where c is not divisible by 2…

A: Fundamental Theorem of Arithmetic: Every positive integer (except n=1) can be uniquely expressed as…

Q: ab = a – b is a commutative binary operation on Z

A: A binary operation * is called as commutative if for all a,b a*b=b*a

Q: Show that 1 Is En=1 2 1?+ 1 4

A: (Solving the first question as per our guidelines) Solution: The series is ∑n=1∞1n2+1 Split the…

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: Suppose a, b, and c are integers and suppose a |b and ałc, where a{c denotes that c is not divisible…

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Q: Suppose a,b are nonzero integers. Then gcd(a,b) = min{ma +nb : m,n ∈ Z and ma+nb > 0}. Furthermore,…

A: The finest not unusual place divisor (GCD) of or greater non-0 integers is the biggest fantastic…

Q: Consider the following Cayley Table defined by the binary operation M. M y y y y y а. Is M…

A: (a). Since the Cayley table is symmetric about the principal diagonal, so M is commutative. (b).…

Q: 2. Let S be the set of three elements given by S = {A, B, C} with the following table. * A B A A B B…

A: From the given table , we can see that  A*B=B= B*AA*C=C=C*AB*C=A=C*B So, the binary operation * is…

Q: Which of the following binary operation is not closed in the set of real numbers? O a*b = √ab O a*b…

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Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

A: NOTE- AS PER POLICY I  HAVE CALCULATED FIRST MAIN QUESTION ONLY. Here Given 4 digits 1,2,3,4

Q: The binary operation defined as a*b=3a 2b is closed in all the given sets EXCEPT | O set of Natural…

A: Given operation is a*b = 3a - 2b

Q: (S, *) is said to be algebraic binary structure if (A) * is binary operation on S (B) * is…

A: Solution:

Q: The binary operation is defined by the following below table on set G = {a, b, c, d}. Test 1- If…

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Q: Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example…

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Q: Prove that if a is a positive integer, then 4 does not divide a2 + 5.

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