Does the relation "is a friend of" have a reflexive property (consider one person)? A symmetric property (consider two people)? A transitive property (consider three people)?

Q: What is the equivalence of ( ¬ (( P → Q) ∧( Q → P))) ↔ ( Q → P)?

A: the equivalence of ( ¬ (( P → Q) ∧( Q → P))) ↔ ( Q → P) is to be computed below .

Q: Show that (r ∨ ¬s) ∧ (r ∨ s) ≣ s using logical equivalence laws

A:

Q: If P(A)=p, P(A|B)=q, P(B|A)=r and A,B are mutually exclusive then what is the relation between p,q…

A: Let A and B be two events which are mutually exclusive. The probability that event B occurs provided…

Q: qV[~(q^r) ~q]

A:

Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: What is the natural domain?

A:

Q: Let A = {2,3,4} and B = {2,6,8} and let R be the “divides” relation from A to B Draw an arrow…

A:

Q: The midpoint of (5, 5) and (5, 5) is (5, 5). O True O False

A: topic - coordinate geometry

Q: Given the relations on the set of real numburs, &, - E(G,6) ER; a>b3, Rq = {CaL) EE, az6} Rs ={(a14)…

A: GivenR1=a,b∈R2 , a>bR2=a,b∈R2,  a≥ba) we know that R1+R2 contains thoseelements which are either…

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R reflexive?…

A: In this question we have to explain Is the given relation is reflexive.

Q: 1. List the domain and range for the relation. {(11, -5), (-10, 15), (3, 5), (7,-5)} O Range: {-5,7,…

A: Domain is the values of x and range is the values of y in ordered pairs ( x , y )

Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

A:

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition:  A reflexive relation is the one in which every element maps to…

Q: B. Can the proposition (Vx, y, P (x = y) → (P(x) → P(y))) be proven using the equality axioms?

A: Look at the following equality axiom. ∀x,y, and any function f,x=y⇒fx=fy

Q: Let A = {a, b, c} and B = {r, s, t,u}. Furthermore, let R = {(a,s), (a, t)}, (b, t) be a relation…

A: Step:-1 Given that A=a, b, c,  B=r, s, t, u And R=a, s, a, t, b, t that is,  Hence,  Domain of R =…

Q: Determine if each form is a tautology, a contradiction, or a contingency:

A:

Q: 1. Express the following relations as a table and digraph. а. {(1,2), (1,3), (1,4), (2,1), (3,3),…

A: Relations as a table and digraph According to our guidelines,we can answer only first question.…

Q: Is this correct? Develop a loğical argument.

A:

Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

A:

Q: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

Q: In  a scout camp each girl is familiar with exactly 10 boys and each boy is familiar with exactly 10…

A: Let G be an r-regular bipartite graph, r≥1 with particle sets U and V. Then U =V .

Q: (p^ (~(~pV q))) v (pAq) = p.

A: Few notation for the problem. p∧q : p and q [ This will be true if both p and q are true] p∨q : p or…

Q: The reflexive property of equality is used to demonstrate a segment has the same length as itself. O…

A: Here is the solution of the given problem.

Q: Determine whether the following statements are true or false. If it is true, explain why. If it is…

A: a)   If F(x) is antiderivative of f(x) that is  ∫fxdx=Fx+C      Then for antiderivative of f(ax)

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

A:

Q: How to express the commutativity of V as a tautology?

A:

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

A:

Q: (p^ (~(~pV q))) v (pAq) = p.

A: Introduction :-  Given :-  We have to show logical equivalence of two statement patterns.

Q: Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.

A: Number of elements in A=2 ...................................In B=2

Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

A:

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: Which of the following is NOT commonly used as inferential tool?

A: Inferential statistics deal with data taken from a sample and makes inferences about the larger…

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: - In computer science, a binary relation called the exclusive or is often used and notated by ®.…

A:

Q: Construct the semantic tableaux for each wff to determine whether an equivalent wff exists that…

A: p∨q∧r∧~p∨~q∧~r                 ⋮p∨q∧r,~p∨~q∧~r      ⋰⋱                ⋰⋱    p   q∧r     ~p   ~q∧~r…

Q: The statement (H ⇒ B) ∧ (¬B ∨¬D) is considered a valid argument: true or false?

A: Introduction: The validity of an argument is resoluted base on its truth value. When an argument is…

Q: What is the domain of the relation (8, 2), (6, 4), (4, 2), (2, 4)? O 2,4 O 2, 4, 6, 8 O 6, 8 O 2, 4,…

A: Concept: Domain is the set of all first elements of ordered pairs (x-coordinates).

Q: Coot R be the relation A = S 2, 34 S,,73 de fned the ゲ rule Cab) ER if the wlese Carbs dixindle the…

A:

Q: State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric,…

A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

Q: If an expoential relation such as y=bx, if b > 0 and b ≠ 1, then the y intercept is at zero. Is this…

A: The given problem is to check whether the y intercept is at zero is true or false.

Q: The domain is {A, B, C, D, E, F, G, H}. The relation is the set: {(C, B), (D, C), (C, F), (G, H),…

A: Given domain is A, B, C, D, E, F, G, H   The relation is the set C, B, D, C, C, F, G, H, F, B, A, B,…

Q: In N × N clause β for (a,b), (c,d) ∈ N × N defined as: (a,b)β(c,d) = ad = bc Examine the properties…

A:

Q: R = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6 e (yes or no) whether R has…

A:

Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

A:

Q: axayP(x, y) is true when P(x, y) is false for every pair x, y. A True В False

A:

Q: Construct the semantic tableaux for each wff to determine whether an equivalent wff exists that…

A: According to the given information, first it is required to make the semantic tableaux for the given…

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

A:

Q: i. Determine whether (-p^(p→q)→~q)is a tautology.

A: Hello. Since your question has multiple questions, we will solve the first question for you. If you…

Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6