3. Prove that if a is an . odd number and b is an integer then b² a² +9.

Q: An operation * is defined on the set of real numbers by a * b = a + b – ½ ab. What is (3 * 2) * 2? *

A: The rational number and irrational number are together called real numbers. An operation is a rule…

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: 32. Prove that 3 divides n³ +2n whenever n is a positive integer.

A:

Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

A:

Q: Determine a conclusion. Choose the correct answer below. the null hypothesis. There is difference…

A: That is, there is no evidence to conclude that there is significant difference between the two…

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: Which of the following is a binary operation on the set of positive real numbers? a. a*b = √a + √a+…

A:

Q: . Homework. Let a and b be integers. If 7 | (17a +256), prove that 7 | (10a+11b).

A:

Q: 5. Show that 2 32 3" 31 3" for all positive integers n.

A:

Q: Let 2 A = 3 and B = -3 Show that AB # BA.

A: Given, A=1232,  B=2-1-34

Q: Find the product of all positive integers from n down through 1 for n = 5.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3. Let x be an integer. Use the previous result to prove the following corollaries. (a) If x divides…

A: Divisibility: If a and b are integers, we say that a divides b, and write a|b, if there is an…

Q: If AB = BA and p is a nonnegative integer, show that (AB)p = A p B p .

A: Given p is non-negative integer AB=BA

Q: Prove or Disprove: If x is an integer and 7x³+9 is even, then x is odd.

A: According to the given information, it is required to prove or disprove the given statement.

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Show that 3·4n+ 51 is divisible by 3 and 9 for all positive integersn

A: Consider the provided expression,

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

A:

Q: Show that AB = O, even though A ≠ O and B ≠ O.

A:

Q: 12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

A: We will prove this as following.

Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

A: Let n be an integer. To prove that for any integer n the number 10n+4 is even. An even integer is…

Q: 10. Which of the following are roots of x3- 3x²– 45x-81? -3 and 9 -4 and 8 -2 and -1 -1 and 9

A: Simplification

Q: Let * be the operation on the set of real number defined by a * b = 2a + 4b – ab. (a * b) * c = А.…

A: Operation * is defined by a*b=2a+4b-ab for all real number we have to find the value of (a*b)*c…

Q: #5 Find An if n is a positive integer and A = 4 -3 - 2

A:

Q: Show that if a,b, and c≠0 are integers, then a∣b if and only if ac∣bc.

A: We have to prove the following statement -  If a,b, and c≠0 are integers, then a∣b if and only if…

Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

A: From the given information we want to find How many positive integer solutions are there to x1 + x2…