3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a > c) or (a = c and b > d) is partial ordering relation.

Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: Let A = {1, 2, 3, 4, 5}. Define the following relations on A. R1 = {(1,1), (1,2), (2,1), (3,2),…

A:

Q: Consider the partial order with domain{3,5,6,7,10,14,20,30,60}and with x ≤ y if x evenly divides y.…

A:

Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

A:

Q: Draw the direction of the graph that represents the relations.

A: We need to draw the directed graph which is represented by the given relation,…

Q: Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x…

A: Since the questions contains many subparts. As per the guidelines I am answering the first three…

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

A:

Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

Q: {(a, b) acb, a and b are finite set of integers}

A:

Q: 26. Use Algorithm 1 to find the transitive closures of these relations on {a, b, c, d, e}. a) {(a,…

A:

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

A:

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

A:

Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: Let A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

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: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a&gt;c or a=c and b≥d Show…

Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

A:

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A| < [B|…

A: A partial order relation is total order relation if each of the pair of the elements are comparable.…

Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

A:

Q: 4.4.5 Write out the following relations as subsets of the Cartesian pod (a) The relation on N…

A: (a) The relation given is already a subset of the Cartesian product N x N. It can be written as…

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

A:

Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…

A:

Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Let S = ((a), b, (a, (b)]), c). Which one of the following relations on S is a strict partial order?…

A:

Q: Prove or disprove: If R and S are partial orderings on A, then R ∩ S is also a partial ordering on…

A: Partial order relation of intersection of two partial order set

Q: 1), consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)…

A:

Q: List elements of S(partial ordering relation).

A:

Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}.…

A:

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

A:

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

A:

Q: For every nonempty set A, there exists a relation R which is both an equivalence relation and a…

A: A relation R is said to be equivalence relation if R is Reflexive ,Symmetric and Transitive . R is…

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Let A = {1,2,3,4}, B = {2,3,4,5}, and C = {2,4,6,8,10}. Suppose R is a 3-ary relation that is…

A: To determine the triples in the array.

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

A:

Q: 1. Identify the domain of the relation: 其-5 |-2| 1 10 11 4 10 а. -5, 10 b. 10, 11, 4, 10 C. -5, -2,…

A: We have to find the domain of function

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or A=B.

Q: Consider the following binary relation: Vx, y E R?, x Ey if x1 > Yı (indepen- dent of x2 and y2) or…

A: We will use the basic knowledge of relations to answer this question correctly and completely.…

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

A:

Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information:

Q: Let B = {1, 2, 3, 4} and S be the relation defined by S = {(1,1), (1,3), (1,4), (2,2), (2,4), (3,3),…

A: Let B = {1, 2, 3, 4} and S be the relation defined by S = {(1,1), (1,3), (1,4), (2,2), (2,4),(3,3),…

Q: 11. List the domain and rage for the relation. 4 -6 13 O Range: { 4, 2, 6, 7} O Domain: { 4,2,6, 7}…

A: Please refer the attached image for complete Solution.

Q: For any partial order there may be a number of linear orders that are consistent. For example, for…

A: This is a question from Relation.

Q: A) List all reflexive relations can be defined on set {a, b}. B) List all ordered pairs in the…

A:

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: How many different partial orderings can we define on the set A = (x, y}? How many different total…

A: 1) The partial ordering of a two-element set must contain the following conditions: a) Reflexive…

Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an crder relation…

A: A partial order relation leads to poset which is very interesting.

Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.