cos(ry) – 1 1. lim(7,9)→(0,0) no existe. sin(2æ) – 2x + y 2. lim(z,y)¬(0,0) no existe.

Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

Q: Let S = {(r.y) R²: (x-1)² + y² ≤4 and y> √3}. Question a. Find the interior, exterior and boundary…

A:

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Prove that for any sets A, B, X - X − (An B) = (X − A) U (X – B). -

A: .

Q: Use an algebraic proof to show that for all sets X ,Y and Z : (X – Y)n ZC = x – (Y u Z) Do not…

A:

Q: 1. Let A = [1, 3], B = (2, 5], and C= {2}. Write the inequalities (or equalities) that specify each…

A: We will just use of definitions of different type of sets

Q: For Exercise, write the set as a single interval. [(-0, 6) U (10, o)] N [8, 12)

A: We will draw them on a number line. Draw:

Q: Let A and B be arbitrary sets. For each statement below, decide whether it is true or false. If the…

A:

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

A:

Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

A:

Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: Identify which sets are equal A = {0,1,2} B = {x ∈ R | -1 ≤ x < 3} C = {x ∈ R | -1 < x < 3} D =…

A: We identify which sets are equal.

Q: Given the sets C = {1, -3} and D = {2, 3, 6}, find all ordered pairs (x,y)and those that satisfy the…

A:

Q: Let P be the set of points that belong to the shaded region imaginary The set P is (A) open (B)…

A: Explanation of the answer is as follows

Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: We are given  that R is a transitive relation on a set A  Transitive Relation  A relation on a set X…

Q: (a) (AUB)\C= (A \C)U(B\C)

A:

Q: 3. Prove the triangle inequality: For any real numbers x, y, |x + y ≤ |x| + |y].

A: For any real number  we have to prove

Q: If X, Y are finite sets with |X|=4>2= |Y. How many surjective functions f: X→ Y are there? 2 16 8 O…

A: Let us solve above problem

Q: Let A, B, and C be sets. Prove that: Ax (B\C) = (A × B) \ (A × C).

A:

Q: 4. Find the perimeter of a rectangle whose area is 84 m². The length is 5 m more than its width.

A: Let the length is L and width is b. Given: L=b+5 Area of a rectangle=84m2 As we know that the area…

Q: The set {xER | x 220 or − 3x > 1} can be expressed in interval notation as:

A: Given : {x∈ℝ|x-2≥0  or -3x&gt;1}   To write : Given set in interval notation

Q: (a) For all sets A, B, C, A × (BU C) = (A × B) U (A × C). (b) For all sets A and B, P(AUB) ≤ P(A)…

A:

Q: Provide examples of sets A and B where strict inequality sup(A+B) < sup A+ sup B holds.

A: We have to given an example to prove given inequality:

Q: A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a…

A:

Q: 2. Classify each of the following sets as open, closed, neither, or both. Then, find the closure. a)…

A: classify the given sets are open and closed.

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

A:

Q: a Are ALL the following three pairs in the relation R: (4.2) (1,2) (5,1) b Is 4 a minimum element?…

A: R=4,21,2,5,1a. (1,2) is not the element of R because from Hass diagram 2 is related to 1    here…

Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

A: