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 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: 4. Write as a single power first, if possible, and then evaluate. a) 5³ x 5 b) 4⁹ ÷ 47 c) (2¹)² -5 •…

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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: S: Please answer all the subparts correctly as they are both connect in the same questions in word…

A: We are going to prove that the product of two consecutive integers is even.The product of two…

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: Exercise 6D Use this Venn diagram to answer Questions 1 and 2. Members of youth club (U) Greg lays…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If a and b are positive integers, which of the following can never be the gcd(56a, 63b)? (а) 56а (b)…

A: given a and b are positive integers,  and to find gcd(56a, 63b) gcd of (56, 63) is 7  so gcd(56a,…

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

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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: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

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

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Q: 72c2K+7) ニ72C2K+72)

A:

Q: Determine whether the integer is prime or composite a.) 97^2 + 8 b.) 433

A: Topic = Algebra

Q: Define the binary operator* by: a+b = a +8b and V by: aVb=6 Find the following. When simplifying,…

A: Given operators: a * b = a + 8b   .......(1)  a ∇ b = 6    .......(2)

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: Find 2's complement of 001011011001100

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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: Let the binary operation *

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

Q: -2x 6. A) Find dx 2x 1.

A: We have to find derivative

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: how: For all integers and , if n-m is even then  n^3-m^3  is even

A: We have given that for all integers n,m (n-m) is even.

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

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Q: How many zero divisors are in Z,, where n = 32547?

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

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Q: Evaluate [√3+1¹⁰

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

A: