4. Let R be a relation on the set {1,2, 3, 4} such that R = {(1, 1), (1, 3), (2, 2), (2, 3), (3,2), (3, 4)}. Represent R using a matrix and a directed graph.

Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: d. Define a relation R on {1, 2, 3, 4} by R = {(a, b) / a +b is even} and i. Write R as a list of…

A: According to the given information, Let R be a relation on {1,2,3,4} defined as:

Q: Let A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P), (R, P), (S,…

A:

Q: 9. Represent the following relations on A = {1, 2, 3, 4, 5, 6} using a matrix and a digraph. (a) R =…

A: Given that ,  A = { 1,2,3,4,5,6}

Q: Q4. Let A = { 1, 2, 3, 4, 5, 6} and relation R on A defined by R = { (x,y)|(x+y) is a divisor of 24…

A: A=1,2,3,4,5,6 and relation R on A defined by  R=x,y| x+y is a divisor of 24 So,…

Q: Consider the relation R = {(0,0), (1,1). (2,0), (2.2). (2,3). (3,2). (3,3)} on the set 5 =- {0, 1,…

A: Concept Used:- A relation R is a Partial Order if R is reflexive, anti symmetric, transitive.…

Q: the transitive closure of R = { ( a ,b ), ( a, d ), ( b, c ), ( c, b ), ( c, d ), ( d, b ) }. In…

A: R = {(a , b), (a , d), (b , c), (c , b), (c , d), (d , b) Transitive closure is {(a,b) , (b,c) ,…

Q: 7 Determine whether the set {1, x, x²} is linearly dependent or in- dependent in R (Justify your…

A:

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B?…

A:

Q: Let R be the relation represented by the matrix M₂ [011] Γοιι 110 101 Identify the matrix that…

A:

Q: Find the adjacency matrices for the directed graphs in (a) and (b). (a) V3 V1 V2 For the adjacency…

A: Rematch: The given graphs in (a) and (b) are not diagraphs (because no edges are directed with…

Q: Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence…

A: P={{a,b,d},{c,f},{e,g}} . The  equivalence relation is as follows:…

Q: Draw the directed graph of the relation R on A = {1,2,3,4,5,6,7,8} defined as R = {(a,b)|a,b e A and…

A: Here, the relation is: R=(a,b)|a,b∈A and a≡b mod 3 That is: a-b is divisible by 3. So, 7-1=6 is…

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

A: Given that, A=a,b,c,d,e And R=(a,b),(b,c),(b,d),(b,e),(d,e) The graph for the diagram is,

Q: Let C denote the set of all ordered pairs (a, b) with a,b & R. L.e., C:= {(a,b): a,b € R}. Define…

A: NOTE: According to guideline answer of first three related subpart can be given, for other please…

Q: Let A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)}…

A: Given :  A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)}…

Q: Draw a directed graph for the relation R on the set {0, 1, 2, 3) given by 10. R = {(0, 1), (0, 2),…

A:

Q: r1 1 1 0- 1 0 0 c) The matrix M represents the relations R defined. = 1 1 11 the set A = {1, 2, 3,…

A:

Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

Q: (b) Let A = {1,2,3}. Consider the relation R on A given by R = {(1,2), (1,3), (2,1), (2,3), (3,2)}…

A:

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

A:

Q: 1. By using the attached graph of relation R1.  a) Express R1 as a set of ordered pairs. b) create a…

A:

Q: We have two sets A= [5, 7, 9, 11] and B= [4, 8, 12, 15, 18]. Relations from these sets are [5, 8],…

A:

Q: Let 4= {1, 2, 3, 4, 5, 6} and the relation R on A is defined by R = {(a,b)|a + b is prime; a, b E A}…

A:

Q: Q3) Consider the relation R = {(1,3), (1,4), (3, 2), (3, 3), (3, 4)} on A = {1,2, 3, 4} a) Find the…

A:

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: The relation R=((a,a),(b,b)) on set X=(a,b) is. transitive symmetric reflexive anti-symmetric None…

A:

Q: Draw a directed graph diagram for relation S on {0, 1, 2, 3,4}, where TSy iff x + y = 4

A:

Q: A.  Write the relation on {a, b, c, d} in matrix form. 1.  {(a, a), (a, d), (b, c), (c, d), (d, a),…

A: The matrix form of a relation is given by M=Mij , where Mij=1    if ai,bj∈R0    if ai,bj∉R Part(1)…

Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

A:

Q: 6) 13. Let S = {a,b,c,d}. Let r be the partial order {(a,a),(b,b), (c,c),(d,d),(b,d),(c,a)}. Give…

A: (6) 13. Let S = {a,b,c,d}. Let r be the partial order {(a,a),(b,b), (c,c),(d,d),(b,d),(c,a)}. Give…

Q: a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the…

A: let A={1,2,3,4}   aRb iff 2a>b+1   first we will find R…

Q: B A' B' Which of the following matrices is T'?

A: We have  to find translation  matrix