# Consider the following theorem: “If n is an even integer, then n + 1 is odd.” Give a Proof by Contradiction of this theorem.

5,255 results
1. ## Math Proof

Prove that square root of 12 is irrational. **I don't know if I did this correctly PF: By contrapositive, assume sqrt(12) is rational. Then there exist an a,b as integers such that a/b is written in the lowest terms, and sqrt(12)=a/b. Then by squaring both

2. ## maths

1. If the first and third of three consecutive odd integers are added, the result is 51 less than five times the second integer. Find the third integer. Let the 3 numbers be x, (x + 1) and (x + 2). Then, x + (x + 2) = 5(x + 1) - 51 Solve for x. We want

3. ## math

U= { all positive integer less than or equal to 30} M={all even positive numbers less than or equal to 20} N={all odd number less than or equal to 19} S={all integer x: 10

4. ## math

which expression represent the product of 2 consecutive odd integers where n is an odd integer? 1)n(n+1) 2)n(n+2) 3)n(n+3) 4)2n+1

5. ## math

If n is an integer, which of the following must be odd? a. 3n-5 b. 3n+4 c. 4n+10 d. 4n-5 e. 5n+7 please answer and explain

6. ## Math

If m and p are positive integers and (m + p)x m is even, which of the following must be true? Would it be: (A) if m is odd, then p is odd. (B) if m is odd, then p is even. (C) if m is even, then p is even and (D) if m is even, then p is odd. I had chosen D

7. ## Geometry

Working on conjectures. The question is Conjecure: The product of any two odd numbers is _____? It shows several examples of odd numbers x odd numbers and the products are all odd. So I think the right answer is "odd numbers" but is there some formula I

8. ## help me plz

if a and b are both odd integers, which expression must always equal an odd integer? 1 a+b 2 a*b 3 a-b 4 a/b

9. ## math

M is an odd integer. For each of the following numbers, check if the number is odd. 2m- 1 2m +1 m^2 - m m^2 +m+1

10. ## Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = √x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b) Yes, x=16/9 c) Yes, x=1/4

11. ## Mathematics

Consider the following theorem: “If n is an even integer, then n + 1 is odd.” Give a Proof by Contradiction of this theorem.

12. ## maths

P and Q are subsets of the universal set U defined as U={x:x is an integer and 1

13. ## Algebra 1 Polynomials

Suppose n is an integer. Select all statements below that are true: (choose 3) A) n^2 + n is always an even integer*** B) n^2 + n is always an even integer when n is even*** C) n^2 + n is always an even integer when n is odd*** D) n^2 + n is never an even

14. ## Math

The sum of two consecutive odd integers is 52. State the odd integer x

15. ## math

if the number represented by n-3 is an odd integer, which expression represents the next greater odd integer? a n-2 b n-1 c n-5 d n+1

Did I get this practice question right? 1. Consider the following functions: f(x)=cos(x^3-x) h(x)=|x-3|^3 g(x)=1n(|x|+3) s(x)=sin^3(x) Which of the following is true? (Points : 1) f is even, h and s are odd. ***f and g are even, s is odd. h and s are odd,

17. ## Abnormal Child Psychology

Which of the following is true regarding the relationship between ODD and CD? A. most children who display ODD go to to later develop CD. B. There's no relationship between ODD and CD. C. CD is almost always preceded by ODD. D. ODD is almost always

18. ## discrete math

use a direct proof to show that the product of two odd numbers is odd. Proofs: (all the nos. i used are odd) 3 x 3 = 9 5 x 9 = 45 7 x 3 = 21 Yes, but you didn't prove the statement for "all" odd integers, only the odd integers you selected. uhm..he didn't

19. ## Math

We call a natural number "odd looking" if all its digits are odd.How many 4-digit odd looking numbers are there?

20. ## pre-algebra

The perimeter of a triangle is 195 mm.If the lengths of the sides are consecutive odd integers,find the length of each side. what steps do i need to do in order to get the answre? Perimeter= L + L+2 + L+4 solve for L. That is the short side. THen add two

21. ## math

Show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer

22. ## Algerbra

f m and p are positive integers and (m + p) x m is even, which of the following must be true? A. If m is odd, then p is odd. B. If m is odd, then p is even. C. If m is even, then p is even. D. If m is even, then p is odd. I choose C is that correct

23. ## Algebra

The sum of two consecutive odd integers is 56. A. Define a variable for the smaller integer. B. What must you add to an odd integer to get the next greater odd integer? C. Write an expression for the second integer. D. Write and solve an equation to find

24. ## algebra 2

consecutive odd integer problem find two odd integers the sum of whose squares is 130. (sq)=squared let x= 1st odd int let x+2=2nd odd int (2x+2)(2x+2)=130 4x(sq) + 4x+ 4x +4=130 4x(sq) + 8x -126= 0 2(2x(sq)+4x-63)=0 My question: the two numbers to factor

25. ## Math

find four consecutive odd integers such that the sum of the least integer and greatest integer is 164

26. ## Pre-Algebra

Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second. let X = 1st odd number. and Y = 2nd odd number = X + 2 since it is consecutive. Now set up two equations (the first is Y = X + 2). The second is 5X =

27. ## Math

Find three consecutive odd integers such that four times the middle integer is two more than the sum of the first and third.

28. ## discrete math

prove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start with If n is an integer and

29. ## algebra

Kayla Wants To write an Expression that will always produce an odd integer. Which of the Following will always produce an odd integer for any given integer ?

30. ## maths

1. If the first and third of three consecutive odd integers are added, the result is 51 less than five times the second integer. Find the third integer. 2. Write as a subtraction problem and evaluate. 15 less than -2 n, n+1, N+2, ... are consecutive

31. ## math

show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer.

32. ## DISCRETE MATHS

Prove that if n is an odd positive integer, then 1 ≡ n2 (mod 4).

33. ## math

in lotto draw balls 1-50 mixed together. machine randomly selects numbers 13,11,7,27,41. is the 6th number drown A. more like to be odd than even b. more likely to be even than odd c. equally likely i could not decide, as long as there even and odd

34. ## Algebra

The sum of two consecutive odd integers is 24. Which equation can be used to find the first integer n? F. n + 1=24 G. n + 2=24 H. 2n + 1=24 I. 2n + 2=24

35. ## math

Find three consecutive odd integers such that four times the middle integer is two more than the sum of the first and third. I think I'm doing it wrong. 4((x)+(x+2)=x+(x+4)+2 4(2x+4)=2+3x+6 8x+16=3x+8 5x=8 ? Please help

36. ## Maths

The first odd number can be expressed as 1 = 1squared - 0squared. The second odd number can be expressed as 3 = 2squared - 1squared. The third odd number can be expressed as 5 = 3squared - 2squeared. a) Express the fourth odd number in this form. (Am I

37. ## math

Which of these is a rational number A.)integer 150 B.)integer 441 C.)integer 200**** D.)integer 250

38. ## Math - Calculus

Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? ...Other than simply using my TI-84, I have no idea how to accomplish this.

39. ## discrete math

Prove by contradiction that for any even integer a and any odd integer b, 4 does not divide (a^2 + 2b^2). Proposition: That 4k (k is any integer) = a^2 +2b^2, and a is even, and b is odd. But 4k is even (product of any integer and 4), so a^2 must be even,

40. ## Algebra

Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second. I've gotten this far but confused as to what the two intergers are. 5x=3(x+2)=12 5x=3x+2+12 5x=3x+14 2x=14 2x/2x=14/2 x=7 Let n be first integer, so

41. ## Math

Let a, b, and m be integers, and m ≥ 2. Prove that: ab ≡ [ (a mod m) · (b mod m) ] (mod m). So I tried proof by cases: Assume ab ≡ [(a mod m) ∙ (b mod m)] mod m is true. Then ab mod m = [(a mod m) ∙ (b mod m)] mod m, and (ab-[(a mod m) ∙ (b

42. ## algebra 2

consecutive odd integer problem find two odd integers the sum of whose squares is 130. (sq)=squared let x= 1st odd int let x+2=2nd odd int (2x+2)(2x+2)=130 4x(sq) + 4x+ 4x +4=130 4x(sq) + 8x -126= 0 2(2x(sq)+4x-63)=0 My question: WHAT ARE THE TWO DARN

43. ## maths

the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, añ = b[√(n+c)] +d. Where [x]

44. ## math check

2.)The sum of four consecutive odd integers is -336. Set up an equation AND solve for all of the integers. Two ways to approach this. -336/4 = -84 making the 4 consecutive odd numbers -81, -83, -85 and -87. Alternatively: x + (x + 2) + (x + 4) + (x + 6) =

45. ## Math - Fundamental Theorem

We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate pairs). But how can we get the

46. ## Algebra

If r is an integer greater than 1, what is the value of (−1)^r +1 if: 1. r is an odd integer 2.r is an even integer

47. ## math

A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is

48. ## Math

1. In an ordered set of 4 consecutive odd integers, the sum of 3 times the second integer and the greatest integer is 104. Which is the least integer in the set? Choices: 11, 17, 19, 23, 27 2. How old is David if his age 6 years from now will be twice his

49. ## Math

If 7y+9 represents an odd integer, which of the following represents the next smallest odd integer? a. 7(y-2)+1 b. 7(y-2) c. 7(y+3) d. 7(y+2) e. 7(y+1)

50. ## odd and even functions

Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x) for all real x, how do I 1)show that a polynomial P(x) that contains only odd powers of x is an odd function 2)show that if a polynomial P(x) contains both odd and even powders of x, then it is

51. ## Calculus

Verify the hypothesis of the mean value theorem for each function below defined on the indicated interval. Then find the value “C” referred to by the theorem. Q1a) h(x)=√(x+1 ) [3,8] Q1b) K(x)=(x-1)/(x=1) [0,4] Q1c) Explain the difference between the

52. ## Math Calculus

The Image Theorem: The image theorem, a corollary of the intermediate value theorem, expresses the property that if f is continuous on the interval [a, b], then the image (the set of y-values) of f on [a,b] is all real numbers between the minimum of f(x)

53. ## math

John stated that when you add an even and an odd integer the answer will be odd. Use these numbers to answer the questions: –13, –8, 16, 23, –7 Is John’s statement always true, sometimes true, or always false? Write two equations to support your

54. ## Geometry

Could anyone tell me if this question is correct? 2.) Which is true about both Pappus's Theorem and Desargues' Theorem? Each theorem applies to spherical geometry. Each conclusion states that three points are collinear.

55. ## Discrete Mathematics

Prove that if n is an odd positive integer, then 1 ≡ n(power of 2) (mod 4).

56. ## math

I know It's probably an easy question but I don't know remember how to do it. Show the work to determine if the relation is even, odd, or neither. a ) f(x) = 2x^2 - 7 b) f(x) = -4x^3 - 2x c) f(x) = 4x^2 - 4x + 4 If f(-x) = f(x), for any x, the function is

57. ## college Stats

If Y has a geometric distribution with success probability p, show that P(Y= an odd integer)= p/(1-(q^2))

58. ## Math

Suppose that for any integer n, f(n)= (n-1). if n is even; f(n)= (2n). if n is odd. If k ∈ N, and f (f (f(k))) = 21, find the sum of the digits in k I really don't get this means. (∈)

59. ## Geometry

CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to

60. ## Discrete Math

1. Assume that n is a positive integer. Use the proof by contradiction method to prove: If 7n + 4 is an even integer then n is an even integer. 2. Prove: n is an even integer iff 7n + 4 is an even integer. (Note this is an if and only if (iff) statement.

61. ## Algebra

A.Write and solve an equation to find three consecutive integers with a sum of 126. Let n= the first integer. B. In part A, could you solve the problem by letting n= the middle integer,n-1= the smallest integer, and n+1= the largest integer?

62. ## Math Algebra

Two times the smallest of three consecutive odd integers is one less than the largest integer. Find the integers

True or False: If a|b and a|(b + 1), then a = ±1. [NOTE: Use this Theorem 3: If a|b and a|c, then a|(bx+cy) for any integers x and y. PROOF: Since a|b, there is an integer u such that b = au. Since a|c, there is an integer v such that c = av.

64. ## algebra

Find the two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second. can some explain to me how to get this i was thinking the formula would be ' 5x+12=3x No, that's not it. The second integer is x+2, since it is

65. ## Math

John stated that when you add an even and an odd integer the answer will be odd. Use these numbers to answer the questions: –13, –8, 16, 23, –7 Write a rule for adding an even and an odd integer.

66. ## DISCRETE MATHS

We need to show that 4 divides 1-n2 whenever n is an odd positive integer. If n is an odd positive integer then by definition n = 2k+1 for some non negative integer, k. Now 1 - n2 = 1 - (2k+1)2 = -4k2-4k = 4 (-k2-4k). k is a nonnegative integer, hence

67. ## Mathematical Proof

Hello everyone, Trying to get my head around deductions and the deductive step using my text book, could someone look over my work: Question: n+6 is odd if and only if 5n+1 is even. So my working, here it goes: n+6=2k+1 n=2k-5 thus 5n+1=5(2k-5)+1 =2(5k-12)

68. ## algebra 1

PLEASE HELP! NO ONE ANSWERED THE QUESTION three times an odd integer is eleven less than four times the next greater even integer. What is the odd integer?

69. ## Algebra

Solve algebraically using one variable: Find three consecutive odd integers such that the product of the first integer and the third integer is equal to nine more than twelve times the middle integer.

70. ## Algebra Word Problem

Solve algebraically using one variable: Find three consecutive odd integers such that the product of the first integer and the third integer is equal to nine more than twelve times the middle integer.

71. ## algebra

three times an odd integer is eleven less than four times the next greater even integer. What is the odd integer?

72. ## algebra

find three consecutive odd integers such that the sum of the middle and largest integer is 21 more than the smallest integer

73. ## maths

prove that any odd positive integer of 8q+1,where q is any integer?

74. ## algebra

For three consecutive odd​ integers, the sum of 3 times the first integer and 2 times the second integer is 7 less than 4 times the third integer. What are the three​ integers? Separate your answers with commas.​ Ex: 1,2,3 Please show work thank you

75. ## Algebra

For three consecutive odd​ integers, the sum of 3 times the first integer and 2 times the second integer is 11 less than 4 times the third integer. What are the three​ integers? Separate your answers with commas.​ Ex: 1,2,3

76. ## algebra

For three consecutive odd​ integers, the sum of 3 times the first integer and 2 times the second integer is 77 less than 4 times the third integer. What are the three​ integers? Please show work thank of you

77. ## Proofs and numbers

Prove the following theorem: Suppose p is a prime number, r, s are positive integers and x is an arbitrary integer. Then we have x^r identical to x^s (mod p) whenever r is identical to s (mod 11).for x belongs to an integer

78. ## maths

If n is an odd integer, all of the following are odd EXCEPT (A) n - 2 (B) 2n + n (C) n2 + n (D) (n + 2)2

79. ## Pre-Calc/Trig

is the integer n odd or even, explain

80. ## Math

You start with 101 and want to get down to 0 by subtracting 2. How many times will you subtract 2 from 101? 101 is an odd number and 0 is even; you can't get from an odd to an even by subtracting even numbers. If you subtract 50*2, or 100, you'll get to 1

81. ## maths-

if n is an odd positive integer, then prove that n^2 -1 is divisible by 8

82. ## math

suppose T is a right angle whose sides have a b c. is it possible that each of a b c is an odd integer?

83. ## math

Prove that if p, q, r and s are odd integers, then the equation x^10 + p x^9 - q x^7 + r x^4 - s = 0 has no integer roots.

84. ## math

Prove that if p, q, r and s are odd integers, then the equation x^10 + px^9 - qx^7 + rx^4 - s = 0 has no integer roots.

85. ## math

If A={x|x is an odd integer} and B={9,11,12,14} list the elements of A n B. So find the intersection of A and B. Please helpppppp!!!!!!! :(

1. What is the maximum integer n such that 3^n is a factor of the product of all the odd inegers between 1 and 200?

87. ## math

Suppose T is a right triangle whose sides have lengths a, b, and c. Is it possible that each of a, b, and c is an odd integer? Yes No Explain and demonstrate your answer.

88. ## Math (precalculus)

I have a question about the symmetry of graphs, but maybe it's more of a simple factoring question... Why is f(x)=x+(1/x) odd, while h(x)=x-x^2 is neither even nor odd? I understand that f(-x)=-x-1/x=-(x+1/x)=-f(x) is odd because f(x)=f(-x). Then for

89. ## MathLog#4

Simplify: ((2x^n)^2 - 1)/(2x^n-1) where x is an integer and n is a positive interger. for this one igot the answer the same as 2n^x+1, but will the value of the given expression be even, odd, or either? Please explain. :) Thank Yoo

90. ## math

An integer is 5 more than another integer. Three times the bigger integer is 11 more than the square of the smaller integer. find the two integers

91. ## Geometry

5. What theorem do Exercises 1-4 prove? (1 point) Triangle Inequality Theorem Converse of the Angle Bisector Theorem Angle Bisector Theorem Triangle Midsegment Theorem

92. ## Calculus

the function of f(x) = x + sin (x) on the interval [0,b] i have to find b. two values of c that are given are (4.6658, 1.6174) that satisfy the mean value theorem on [0,b] i got b as +/- 3.29 but it has to be an integer so i think that's wrong. ' can

93. ## For <b>marie flore joseph</b>

Please do not add your new question as a response to somebody else's post. click on "Post a New Question" above to post your problem. Here is your question : Math - marie flore joseph, Monday, April 5, 2010 at 10:37pm the difference of the squares of two

94. ## Math - Calculus

Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? ...Other than simply using my TI-84, I have no idea how to accomplish this.

95. ## Algebra

A.Write and solve an equation to find three consecutive integers with a sum of 126. Let n= the first integer. B. In part A, could you solve the problem by letting n= the middle integer,n-1= the smallest integer, and n+1= the largest integer?

96. ## Algebra 2

A pyramid has a rectangular base. Find the volume if the length and the width of the bad and the hight are three convective odd integers and x is the largest integer.

97. ## Algebra

Solve algebraically using one variable: Find three consecutive odd integers such that the product of the first integer and the third integer is equal to nine more than twelve times the middle integer.

98. ## math

write a program that takes an integer n and output the largest odd divisor of n

99. ## calculus

Find the lim x->infinite (x/[3x+5]) where [] denotes the greatest integer function use the squeeze theorem.

100. ## calculus

Verify that the Intermediate Value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x^2 - 6x + 8, [0,3], f(c) = 0 I have no idea how to use the theorem :(