(a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a), (d, d)). It is a fact that R is an equivalence relation on A. How many distinct equivalence classes does R have? Use set - roster notation to write the equivalence classes of R.

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 = {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: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

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: need help

A: Step 1: First find out the (m,n) which belong to the equivalence classes R for x, y ∈ A. As mRn ⟺…

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

A: Equivalence classes of  [a]={a}.   Since only the element "a" is in the relation with "a" .…

Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

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

A:

Q: Suppose R, S are equivalence relations on set A. Prove or disprove that (a) R-¹nS is also an…

A:

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: Let R be a relation defined on the set of integers as follows: a R b iff 6 divides  (a - b). R is…

A:

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

A: Given a set, A=-3, -2, -1, 0, 1, 2, 3, 4, 5, 6. R be relation on A, defined by, R=x, y: 3|x-y, ∀x, y…

Q: aRb, cRd and aRd, then bRc.

A: A relation R defined on a set A is i) reflexive if aRa for all a belonging to A.ii) symmetric if aRb…

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on 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: = Give an example of an equivalence relation R on the set A {a, b, c, d, e, f, g, h} such that there…

A:

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: Define the relation R on 72 = Z x Z by (a, b) R (c, d) if a + d = b+ c. Prove that R is ar…

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: Let S be the set {a,b.c} and the relation R on S is…

A:

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

A: The objective of this question is to find the distinct equivalence classes of the relation R on set…