Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and [4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the digraph representation of R.)

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

A:

Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

A:

Q: Explain why each of the following binary relations on S = {1, 2, 3} is not an equivalence relation…

A:

Q: Let A = {2,3,4,...,17,18). Let R be the equivalence relation on AxA, defined by (a,b)R(c,d) if and…

A: Let A = {2,3,4,.......... 17,18].Let R be the equivalence relation on AXA, defined by (a,b)R(c,d) if…

Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

A:

Q: 2. Let R = {(x, y) = R x R = |x] + [y] =4}. Then R is a relation on R. Is R an equivalence relation…

A:

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: Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements…

A:

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1),  (2,…

A:

Q: Let R be an equivalence relation on A = {0, 1, 4, 5, 7, 9} and R = {(0, 9), (9, 0), (0, 0), (9, 9),…

A:

Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

A:

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

A:

Q: 3) a) Suppose A = {0,1,2,3,4} and R = {(0,0). (0,4).(1.1), (1,3).(2,2).(3,1).(3,3),(4,0).(4,4)} is…

A:

Q: Select the correct statement(s) for the relation R, defined on the set A = { a, b, c, d, e } by R=…

A:

Q: Let A = {1,2,3, 4, 5, 6, 7, 8, 9, 10) and define a relation R on A by a R b if 6. and only if a and…

A: 6. By the definition, a R b iff a and b have the same remainder when divided by 4.     So, obviously…

Q: Let A = {p , q, r, s, t, u, v}, and let R be the following equivalence relation on A: R = { (p, p)…

A:

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

A:

Q: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

A:

Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

Q: Let A = {1, 2,3, 4}. The following relation R is an equivalence relation on A: R=…

A:

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

A:

Q: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

A:

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: Def (Function): A binary relation RCX X Y is called a function from X to Y, written f:X →Y if -…

A: The concepts have been explained with examples.

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: tA {1,2,3,4,5}. Then define the relationR = {(1, 1), (2, 2), (3, 3), (4, = {(x,y) ERXR | |x|+ [y] =…

A:

Q: Discrete Math: Lets say B = {1,2,3,4,5,6}. Let R be the smallest equivalence relation on B which…

A:

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.