. The operation * is defined over the set R of real numbers by a *b = a+b+2ab. What is the identity element under the operation *.

Q: What set is in another class of infinity that is bigger than R?

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: Show by contraposition that for any real number x if - 5 < x< 4 then x2+x – 20 < 0

A: For the solution follow the next step.

Q: Prove that the set of positive integers is equal to the set {1,2,3,...}. (Using Axioms)

A: This is a problem of set theory and cardinality.

Q: What is the set Z+ of all positive integers?

A: Set of integers are represented as: ℤ={.....,-3,-2,-1,0,1,2,3.........} Set of natural numbers:…

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

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A: Introduction: A direct proof is a series of statements, the final of which is the conclusion to be…

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A: Consider the provided question, We need to prove that, a     B-A∪C-A=B∪C-A(b)     A-C∩C-B=∅ We prove…

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A: We have to find the fundamental set of solution.

Q: Exhibit a one-one correspondence between the set of odd integers O

A: Given, O be the set of odd integers and N be the set of natural number.

Q: Find the smallest distinct postive numbers that provide a counterexample to show the statement is…

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Q: 4. Describe all zero-divisors and units of Z6 O ZOQ

A:

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Q: 23. Prove that any integers a,9(a?-3)

A:

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A:

Q: rove that the difference of any two odd integers is even.

A: Even numbers are of the form 2k. Odd numbers are of the form 2k+1, where k is an integer.  Let a and…

Q: Check whether each satisfy a relation property: (ex, transitivty, etc ): > = " < 9 for real numbers

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Q: The set of all numbers in the form a + bi is called the set of_______ numbers. If b ≠ 0, then the…

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

A:

Q: Use the roster method to list the elements in the set: {x|x is a negative integer greater than -5}.

A: Our Aim is to list the element in the set: x|x is a negative integer greater than -5using Roster…

Q: rsection of any collection of com

A: This is a real analysis question. Let (X,d) be a complete metric space with X not ∅. Suppose the…

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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: Find the restrictions on x, if any. Enter your answers as a comma-separated list

A:

Q: The set of all numbers in the form a + bi is called the set of. also called a/an numbers. If b + 0,…

A: We have to fill in the blanks.

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A:

Q: Find a set of four integers such that their order and the order of their absolute values are the…

A: We have to find a set of four integers such that their order and the the order of their absolute…

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

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A: In algebra, there are different set of numbers such as Real numbers, Complex numbers, Rational…

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A:

Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: Define a Proof

A: A proof can be defined as an evidence or data that is used to establish a hypothesis to be true . So…

Q: Show that the operation a*b=1+ab on the set of integers Z, has no identity element

A: Let e be the identity element which exist.  Then, a*e = e*a = a

Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Q: Zu[i] is an integral domain with : 49 elements O 6 elements 121 elements O 9 elements

A: Thanks for the question :)And your upvote will be really appreciable ;)

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A:

Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: rix is A = onto R³ 1-2 3 - 1 8 34. Determine whether th 6-6

A: Follow the steps.

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A: The Number of non negative integral solutions of x1+x2+…………+xn=r, where each of xi≥0 is given by…

Q: Which of the following sets are closed under multiplication?

A: Given: (a) The set of all prime numbers. (b) The set of all even numbers. (c) The set of all…

Q: 5!, called 5_______ , is the product of all positive integers from_________ down through________ .…

A: For any positive integer n, n! is the product of all the positive integers  from 1 to n. That is,…

Q: Suppose that and K are points on the number line. IF JK = 13 and lies at 5, where could K be…

A: Recall: Distance cannot be negative but if you will  get negative that means you will move the…

Q: Prove that the sum of two consecutive odd integers is divisible by 4.

A: Let the two consecutive integers be n and n+2 Then we need to prove that (n)+(n+2) is divisible by 4…

Q: The Archimedean Property says that the set of real numbers have no upper bound. True or False

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Q: Suppose A is a set of real numbers such that 7EA and sup A >7. Must A contain a number grater than 7…

A:

Q: What is the set Z of all integers?

A: The set of all integers is, ℤ=........, -4, -3, -2, -1, 0, 1, 2, 3, 4, ........