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: 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: what is an algebra expresion

A:

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

A:

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

A:

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

A: