Express (4, 10) as a set {x : |x – al < c} for suitable a and c.

Q: A relation R defined on the set of real numbers is such that xRy and yRx = x = y: R is said to be A…

A: There are many types of relations Symmetric Asymmetric Reflexive Transitive

Q: Method of algebra and cite a property used for every step: (Z − Y) − (Y − X) = Z − Y.

A: To prove: (Z − Y) − (Y − X) = Z − Y

Q: Match each interval on the left with its set builder description on the right. O Instructions (0, 1)…

A:

Q: Use the element method and contradiction to prove that for all sets S and T S Ռ ( T - S) = {  }

A:

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F open?

A: A set is open if and only if it contains all of its limit points. Also recall that the union of open…

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

A:

Q: Let X, Y be two sets. Prove that X × Y C P(P(X UY )).

A: It is given that X,Y  be two sets. To show that X×Y⊆PPX∪Y Firstly, we define the set X×Y as, X×Y=x,y…

Q: Fuppose that the relation R indicates whether c articular student is registered for a particular c…

A: In this question, the concept of Relation is applied. Relation The relation is a relationship…

Q: Let X, Y be two sets. Prove that X × Y C P(P(X U Y )).

A:

Q: Consider the following sets in the dictionarv order. Determine which of these sets are linear…

A: We know that Linear continuum is a linearly ordered set S of more than one element that is densely…

Q: let G={2nEIJ.] show that (I, +) = (G₁.)

A:

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x € R: 1/x e A}. 1…

A:

Q: Let X, Y be two sets. Prove that X × YC P(P(X U Y )).

A:

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/xe A}. 1…

A:

Q: 23. Let A be a non-empty set of positive numbers, which is bounded above and let B = {xe R: 1/xe A}.…

A:

Q: If X and Y are finite sets, prove that XY = |X|Y. Here, XY is the set of all functions from Y to X.

A:

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}.…

A:

Q: Let C and D be finite sets and let f: C D and g: D C be two functions such that Vy eD f(g(y)) = y…

A: If there exists an one-one map from D to C then "|D| &lt; |C|" or "|C| &gt;|D|".

Q: Consider the relation S on N defined by uSy + 5|(y + u). Determine whether S is symmetric, reflexive…

A:

Q: Let f(z) be an ODD fanetion. If the point (2,3) belongu to f, then another point likely to (0,0) (2,…

A: Given f(x) is odd function.

Q: Suppose that |x| = n. Find a necessary and sufficient condition on r and s such that (x") C (x*).

A: Given,

Q: Express (4, 10) as a set {x : |x − a| &lt; c} for suitable a and c

A: Write the given interval in inequality form as follows: 4&lt;x&lt;10

Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: Let C and D be finite sets and let f :C → D and g : D →C be two functions such that Vy ED f(g(y)) =…

A:

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First write U and the given set in roster form.

Q: 2- Find the set of lower bounds and the set of upper bounds of the following sets in Q, if it…

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

Q: - List the ordered pairs in the relation R from A = (0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b)…

A:

Q: Let A be a nonempty set and define B={kx : x∈A}, where k≥0 is fixed. Prove that supB=ksupA.

A: Given A be a nonempty set and define B=kx:x∈A where k≥0 is fixed. We have to prove that supB=ksupA…

Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: if f is measurable then - f is messlurable

A:

Q: Let A be a non-empty set of positive numbers, which is unded above and let B = {x e R: 1/xe A}. 1…

A:

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

A: Remark: Completeness property of R: Every bounded above non-empty subset of R has a least upper…

Q: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

A:

Q: Prove that for the sets. B={4x+3|X€Z3 we have A =B

A:

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: 23. Let A be a non-empty set of positive numbers, which is ounded above and let B= {xe R: 1/x e A}.…

A:

Q: Let X, Y be two sets. Prove that X x YC P(P(X UY )).

A:

Q: Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following   must…

A: See the detailed solution below.

Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F closed?

A:

Q: Let the non-empty set S = {x - yv3:x,y ER}, show that S is closed'under multiplication then find the…

A: We have to show that the given set S=x-y3:x,y∈R is closed under multiplication and also find the…

Q: FIND: The set, A, of critical numbers of f.

A:

Q: Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following must be…

A: Option (III) is correct.

Q: Let S be some non-empty collection of real numbers. We know that Vx E S, 3y E S such that x2 y.…

A: In this type of question you need to assume the set of x,y and S that satisfy the condition given in…

Q: Is the set θ={((x,y),(3y,2x,x+y)) : x,y∈R} a function? If so, what is its domain and range? What can…

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: One of the following inegualities holds for every xand y belong to real numbers R. اختر احدى…

A: