6. Given the following relations on the set of all integers where (z,y) = R if and only if the following is satisfied. (Check ALL correct answers from the following lists): (a) x+y=0 OA. irreflexive B. symmetric OC. reflexive OD. transitive E. antisymmetric (b) z-y is an integer A. reflexive B. symmetric OC. transitive OD. irreflexive OE. antisymmetric (C) x = 2y Asymmetric

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

A:

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

A:

Q: Identify the matrix that corresponds to the relation {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)).…

A:

Q: Question 4 (a) Let Ri and R2 be the relations on {a, b, c, d} given by R = {(a, a), (a, b), (c, d),…

A:

Q: Consider the following relations on the set A = {1,2,3,4,5). (c) Rg = {(1,4), (2, 5) , (3, 3), (4,…

A: Consider the given function A=1, 2, 3, 4, 5.

Q: Prove the following set identities: (a) (AUB) nC = (ANC) U (BNC); (b) (AUB) - C= (A-C) U (B-C); (c)…

A: The prove of the identities (a), (b) and (c) are given below.

Q: 7 Part 3 of 4 ! Required information NOTE: This is a multi-part question. Once an answer is…

A:

Q: Explain each step of this proof that C(5, 5) + C(6, 5) + C(7, 5) = C(8, 6): Proof. C(5, 5) + C(6, 5)…

A: The proof of the statement is given in the explanation part.Explanation:Steps and explanations are…

Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: (a) A relation is an equivalence relation if it is, reflexive, transitive, and symmetric. Let D be…

Q: Which of the following does not denote a set?   a. N={x|x≥0} b. S c. {1,2,3} d. 2R3

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

Q: the book is "First Course on Fuzzy Theory and Applications" 3.5 Determine the a-cut relation for the…

A:

Q: Each matrix below represents a relation. The rows and columns are numbered 1 through 3 or 4. Give…

A: We have to find the Arrow diagram and relation as a set of ordered pairs for the Matrices in part a.…

Q: Claim: A majorityof adults would erase all of their personal information online if they could. A…

A: The claim is that majority of adults would erase all of their personal information online if they…

Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

Q: Topic: Sets and Basic Notations Directions:  Do as indicated. Use membership tables to prove that…

A:

Q: ​Claim: A minority of adults would erase all of their personal information online if they could. A…

A: Here we want to express claim in symbolic form.

Q: work): Evaluate the det(A) using any method (but make sure to show your A -2 3 -12 12 -14 19 -20 31…

A: Given:The matrix is given by .To Find:We have to find the determinant of the matrix .

Q: Let A={1,2,3,4}=B, Then write down the relation for P(x,y)=xZy where x,y E A

A:

Q: The following relation on the set {1, 2, 3, 4} that antisymmetric is... 1. OR = {(1, 1), (1, 3), (2,…

A:

Q: 2. (T/F) Given a predicate formula y, if we apply an "equivalence rule" to produce and equivalent…

A: Equivalence rule: The equivalence rule in predicate logic can be defined as two formulas are…

Q: (0. }). (c) C = {p : p is prime). (d) D = (-0, –1). (a) A = (b) B = {-1,1}.

A: A countable set is a set with the same cardinality as some subset of the set of natural numbers. A…

Q: (2) Let's double-check our understanding of set operations (a) Is P(AUB) = P(A) UP(B)? (b) Is B -…

A: We have to solve given problems:

Q: Given sets X, Y and Z, use the set properties to show that (Z - x) n (z-Y)=Z-(XUY), indicate every…

A:

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A:

Q: "Consider the relations R₁, R₂, R3 R4 R5 on A = {1, 2, 3, 4} defined by R₁ = {(1, 2), (2, 1)} R₂=…

A: A relation R on the set A={1,2,3,4} is reflexive if (1,1),(2,2),(3,3),(4,4) are all elements of R.…

Q: (d) How many subsets V of A are there so that 1 € V or VOB= Ø? Explain.

A: This question related to set theory . Solution is given below.

Q: 8 11 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is…

A:

Q: df. Every nonempty proper subset of R is either open or closed.

A: False

Q: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

A:

Q: How many equivalence relations on the set {1, 2, 3}? 1. О З 2. O 6 3. О 5 4. O 4

A: The objective is to find the total equivalence relation on set {1,2,3}.

Q: the lollowing relationships lincar or nonlinear? Explain. (w) The bowling place in under new…

A: Topic - linear and non linear relationship

Q: If A has 4 elements and B has 4elements, then the number of possible relations from A to B is O 24.…

A: