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

Q: Show that if a|b then -a|b.

A:

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: Prove: | a | - | b | <= | a + b |

A:

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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

A:

Q: a b = a - b is a commutative binanry operation on Z

A: Commutative operation means without changing the operation the values doesn't change.

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…

A:

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: Which are binary operations? E xplain who or why not . A) On the positive integers ,that is ,…

A:

Q: Q. 02: (a) Verify the commutative propernties of union and Intersection with help of A = (1,2,3,4),…

A:

Q: Does 2|0? O Yes, because 0 = 0· 0. O Yes, because 2 = 0 · 0. O Yes, because 0 = 2 · 0. O No, because…

A: We have to check

Q: If n is a positive integer prove that 3^(2n) - 26n -1 is divisible by 676

A: if n is a postive integer prove that 3^(2n) - 26n -1 is divisible  by 676

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: Al. b. Find the inverse of 17 modulo 23, if exists. If not, give reasons.

A: The objective is find the inverse of 17 modulo 23 if exists or else give the reason why it does not…

Q: Consider the binary operation ∧ on the set {1, 2, 3, 4, 5} defined bya ∧ b = min {a, b}. Write the…

A: Given:

Q: Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find(i) 5 ∗ 7, 20 ∗ 16.…

A: The given binary operation on N is defined as follows.

Q: Determine the cycle or lifetime (N) of the following congruential generator. Xi+1 = (13Xi + 9) mod…

A: Generally linear Congruantial generator is given as,  Xi+1 = (aXi + c ) mod m  Then it has period or…

Q: Evaluate ∫10(−6f(t)−5g(t)) dt given that ∫200f(t) dt=−4, ∫10f(t) dt=4, ∫200g(t) dt=−10, and ∫10g(t)…

A: Given:∫10-6ft-5gt dt∫200 ft dt=-4∫10  ft dt=4∫200 gt dt=-10∫10 gt dt=5

Q: Let '&' be a binary operation defined on the set N. Which of the following definitions is…

A:

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

A:

Q: In RSA encryption P,n primes and{e,n} public key P.q primes and {d,n} public key P.q primes and…

A: In RSA algorithm, we take two primes, p, q.

Q: Show that ∗ : R × R → R given by         (a, b) → a + 4b2 is a binary operation.

A: Given for all real number a and b

Q: 6. Which of the following is not binary operation? Union Project Set differences Cartesian product

A: Let A≠∅. Then a binary operation ∘on the set A is such that ∘:A×A→A define by ∘(a,b)=a∘b.That is,…

Q: Determine whether the following binary operations are commutative/associative on R2 1. (a,…

A: We want to check associativity and commutativity.

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: 7. Use Boolean Algebra to prove that- A.(B + C ) + A (C + B ) = A

A:

Q: Determine whether the following statements below is true or false. 1. (1/2)2<1/2, and 123 is…

A:

Q: The binary of F1 A0B16 is

A: Hexadecimal can be convert to binary by writing each digit in the form of 4 binary bits

Q: 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…

A: a) -6 b) commutative c) Associative

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

A:

Q: If A= then A2021- A. %3D Select one: O True O False

A:

Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: Define the binary operator by: ab=a² + b² and by: a b = 8a+ 8b Find the following. When simplifying,…

A:

Q: For each operation ∗ defined below, determine whether ∗ is binary, commutativeor associative.(i) On…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Prove that 13n13 +11n is always divisible by 24.

A: We prove this by induction on n.

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: Let the binary operation *

A: Given,          a*b=a+2b where a and b are real numbers

Q: If a is divisible by b, then bq, for some integer q. a

A: See the detailed solution below.

Q: What is element a32 in 2A-3B if 01 B = |-2 -1 6 4] -4 0. 1 A = -1 31 2 -4 6 9. -1 1 21 8. 15

A: To find the element a32 in 2A-3B .

Q: If AB = -BA, then A and B are said to be anticommutative. Are A = 1 and B = anticommutative?

A: Since, we have been given that A=0-110 and B=100-1,then our aim is to show that whether A and B are…

Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

A:

Q: Prove AX(B−C) = (AXB)−(AXC)

A:

Q: The number of 6-bit binary strings is Välj ett alternativ: a. 6 b. 16 c. 32 d. 64 e. other

A: The number of the 6-bit binary string is 64 Since it is a binary string so coded with only 0 and 1…

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

A:

Q: Prove that 3" + 1 is divisible by 4 whenever n is an odd positive integer.

A:

Q: Does 9|54? O Yes, because 6 = 54 O Yes, because 54 = 9 · 5. O Yes, because 54 = 9 · 6. %3D O No,…

A: Correct Answer =&gt;  Option C :- yes, because 54 = 9•5

Q: Which of the following is an associative binary eq Select one: O a. a * b = a b O b. (a b) c= a (b…

A: Option (b) is an associative binary operation.

Q: The greatest common divisor of 9n + 10 and 10n +9 is Oa 10 or 19 оь. 19 O. None d. 1 or 19 Oe. 1

A:

Q: 16. (i) Is the binary operation a *b = a + b – ab commutative for all real numbers a, b? (ii) Is the…

A: