Suppose x is a positive rational number and x? < 2. Let y = 22. Prove that x < y and y? < 2. X+2

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

A:

Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

A:

Q: 2show that O (ir Yational numbers iihot hegigitale

A:

Q: theorem Every Ving Can be imbeobling în aving with

A:

Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: Prove that if x is a rational number andy is an irrational number, then x + y is an irrational…

A: As you have asked the problem ( b) only. I have solved this problem in two steps by showing the…

Q: Prove or Disprove: |Q| = |Q^200|, where Q is the set of rational numbers.

A:

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: If Xo and X, are two numbers with Xo F(X1) O B. F(XO) = F(X1) O C. None of the above O D. F(X0) <…

A: It depends on the conditions; If F is a increasing function then option D is correct. If F is…

Q: Assume P(Z> b) = 0.35 for some number b. Without finding the value of b, what P(Z < – b)?

A:

Q: sin x -dx 1 7/4

A:

Q: Show that there are an infinite number of rational numbers between any two real numbers x and y with…

A: using Archimedean property to prove above therom...

Q: 3. In the domain of real numbers, explain what the following statement says in English. A rational…

A: Given: The given statement ∀x∀yy&gt;x→∃zz is a rational number∧x&lt;z&lt;y To find: we need to…

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: Suppose that m andn are positive integers and b is a real number so that the principal n" root of b…

A: We have been given that nth root of b exists where b is the real number.

Q: 8z z + 3 VI €2.

A: To solve the given inequality.

Q: 21 84 = 1, where x and y are positive real numbers, find the smallest possible y of x + y. If + X…

A: Given   21x+84y=1

Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: The union of two sets A and B is defined as the set of all the elements which lie in set A and set B…

Q: Lemma 2 Ifa and y are distinct rational numbers, then there is a rational number z which lies…

A: Lemma 2: If  and  are distinct rational numbers, then there is a rational number  which lies…

Q: Identify the values of x satisfying both |x - 8| < 7 and [x 10 < 6. (Give your answer as an interval…

A:

Q: If 0<x<4 then a < 6x + 2<b   a= b=

A: In this question, we need to find the values of a and b.

Q: Suppose that x is a negative real number and that x < 1/x. Prove that x < 1.

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: Introduction: The number of elements carried by the operation and executing the results of a…

Q: If x ER, x > 0 and r, s are rational numbers, then (i) x > 0; (ii) for x > 1, x" <xs if r < s

A:

Q: The value of x which satisfy 3x + 1| < - is : 5.

A:

Q: Show that V3 +2/6 is an irrational number.

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…

Q: (7) If x < 0 then 1/x < 0. (8) If 0<x<y then 0 <1/y < 1/x

A:

Q: 6. Prove that x is a rational number if and only if 2x - 1 is a rational number.

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

Q: 5. Solve, and express the answer in interval notation: 17 – 3x| < 13 1. [-2, 0) 2. (-0,-2]U[20/3,00)…

A: