Which are binary operations? E xplain who or why not . A) On the positive integers ,that is , Z^+,a*b=a/b B)On Z^+ ,a*b=a^b c)on Q,a*b=a-b D) On Z ,a*b=ab+1

Q: Find the identity element for the operation * on N defined by a *b=a+b+2, Va,beN al al a 240 does…

A: Let e be the identity element. Hence, it can be written that a*e=a .

Q: Find all possible digits that can be placed in the space so that the numbers is 1,182,1_4

A: Apply the rule for a number divisible by 9.

Q: U = { all real numbers} A = { 10, 11, 12, 13, 14, ...} B = {-3, -2, -1, 0, 1, 2, 3} C = {-1, -2,…

A: This is a problem related to set theory. Based on the general formula we will answer the question.…

Q: n^2 +1 is not divisible by 3 for every integer n.

A: Any integer n can be written in the form of: n=3a+b, where b = 0 or 1 or 2 Case 1: If b=0, n2+1=…

Q: what is an algebra expresion

A:

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: Any integer of the form 12k + 11 is also of the form а) Зт + 1 b) 5m + 2 4m + 3 бт + 1

A: We have to do proper manipulation.

Q: 11. Explain why each of the following is NOT a gro (a) The integers with multiplication. (b) The set…

A:

Q: Suppose a is an integer. Prove that if a^3 is a multiple of 3, then a is a multiple of 3.

A: Let a3 is a multiple of 3 but a is not a multiple of 3.a3 is a multiple of 3Therfore, 3 divides…

Q: Prove that, all integers x and y, x^2-4y≠2  1a. Prove that all numbers of the form 1007, 10017,…

A:

Q: Prove by cases For any integer n, n^2 + 5 is not divisible

A:

Q: Prove the claim that there are no integers j and k such that j^2 + 3k^2 = 8

A: Since both j and k are being squared so if we prove the case for positive integers, that will prove…

Q: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

A: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

Q: If a and b are integers with gcd(a, b) = d Then a gcd %3D -1

A: False.

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

A:

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A:

Q: prove the difference of the squares of two z integers is always divisible by 16 (i.e. z1^2 - z2^2 =…

A: We prove that (z_1)^2-(z_2)^2=16k for some integer k, then we say that divisible by 16.

Q: write a program to evaluate even numbers for [1,10],and [11,20]respectively in matlab

A: Even numbers for [1,10] is given below-

Q: 1. Which of the following represents all real numbers greater than -4 but not more than 8. A) [-4,8)…

A: 1)

Q: Prove that (-1+ iB)" + (-1- i3)" has either the velue 2t! or the value if a B any integer (positive,…

A:

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: 2. Use Fundamental Theorem of Arithmetic to prove that the product of any two odd integers is an odd…

A:

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

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: Let the binary operation *

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

Q: 13. Pier Fermat (1601 – 1665) conjectured that any number F, of the form 2²" + 1 where n is…

A: Fermat number is Fn=22n+1

Q: 7*11*13*15+15 is a _

A: From the given problem:   7×11×13×15+15   As we know that the order of mathematical operations is:…

Q: Let S be the set of numbers of the form { ((-1)^(n + 1)) (n - 1)/(n + 1) } where n is an element of…

A:

Q: Prove that 3a^1 is even if and only if a is an odd integer.

A: In the given question we have to prove that Prove 3a^1 is even if and only if a is an odd integer.

Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

A: