(d) Give the equivalence relation on {a, b, c, d, e} whose equivalence classes give the partition P = {{a,b}, {c, d}, {e}}. (e) You are dividing 112 apples among 5 boxes. What is the smallest number of apples that could appear in the box with the most apples?

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: c) For a set X = {1,2,3, 4, 5}, let P be the partition {{1,3, 4}, {2}, {5}}. In the equivalence…

A: Q1(c) asked and answered.

Q: With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: R —A/R— is a set. You will need, of course, to find a superset of A/R, that is, a class X

A: To prove the given relation, show that as, reflexivity, symmetry, transitivity.

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: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}…

A: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17} For…

Q: How many equivalence relations on A=|42| are there that have distinct equivalence classes of size 4,…

A: Given A=|42| and distinct equivalence classes of sizes 4, 7,7, 8,8, and 8.

Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

A:

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

A: Let A  = {-1,0,1}×{0,1,2,3}  i.e A=…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

A:

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

A:

Q: Show that any 2-cut relation (for > 0) of a fuzzy equivalence relation results in a crisp…

A: Let's take the fuzzy relation: R = 10.800.10.20.810.400.900.41000.10010.50.20.900.51 Fuzzy tolerance…

Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

A:

Q: Suppose R is both an equivalence and partial order relation. Show that every equivalence class of R…

A:

Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx for some non-zero t e R. Given…

A: Sol

Q: 4. Let S = {1, 2,..., 10}. Out of all the equivalence relations on S that have exactly 2 equivalence…

A:

Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx for some non-zero t € R. Given…

A: Sol

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

A:

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

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: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: 5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if…

A:

Q: Let R be an equivalence relation on A = {3, 4, 6, 7,8, 9} and R = {(8,3), (3, 8), (8, 8), (3, 3),…

A: Equivalence class: Consider an equivalence relation R on a set A. The equivalence class of an…

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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:

Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

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: 6. Consider the partition P = {{0}, {-1,1}, {-2,2}, {-3,3},{-4,4},...} of Z. Describe the…

A: Given the partition of Z is P=0,-1,1,-2,2,-3,3,-4,4,....

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

A:

Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

A:

Q: Arithmetical division (+) is binary relation on Z+ ООО

A: '*' is a binary relation on A. If, a*b is in A. For all a,b in A.

Q: There are 20 monomials of degree x2 > X3; (b) the reverse lexicographic order on S induced by the…

A: Lexicographical ordering Find largest i such that Ki-1<Ki Find largest j such that Kj-1<Kj…

Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

A:

Q: 4) Suppose R ={(a,b) €Z×Z:b-a is divisible by 3}, show that R is an equivalence relation on Z.…

A:

Q: The relation defined as x ~ yx ≡ y (mod7) for x, y ∈ Z in Z Write the equivalence classes by writing…

A: Relation R is defined in Z as x≡y(mod 7)  (difference of x and y is multiple of 7) Reflexivity : For…

Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

A: Let R be a relation on a set A. Then R is said to be an equivalence relation if it is reflexive,…

Q: Show that any 1-cut relation (for 1> 0) of a fuzzy equivalence relation results in a crisp…

A: Consider the fuzzy relation: R =10.800.10.20.810.400.900.4100010010.50.20.900.51 Fuzzy tolerance…

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: 9.25. Let A = {1, 2, 3, 4, 5, 6}. The relation R = {(1,1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2),…

A:

Q: What is the correct answer to "There are as many equivalence classes as there are which of the…

A: There are many equivalence classes.

Q: Find the number of different partions of a set (a) with one element (b) with two elements (c)…

A:

Q: (5) Let A={-2,-1,0,1,2}. R is an equivalence relation defined as: for all x,y E A, xRy 2| (x-y?).…

A:

Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…

A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1),…

A:

Statements and Logic

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