An equivalence relation partitions the plane R2 into the set of lines with slope 2. Describe...

An equivalence relation partitions the plane R2 into the set of lines with slope 2. Describe

the relation on R .

Expert Solution

Colby Messinger answered 2 years ago

Show that the given relation R is an equivalence relation on set S. Then describe the...

Show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence classes of R. Let S be the set of all possible strings of 3 or 4 letters, let z = ABCD and define x R y to mean that x has the same first letter as y and also the same third letter as y.

Determine whether the given relation is an equivalence relation on the set. Describe the partition arising...

Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation. (c) (x1,y1)R(x2,y2) in R×R if x1∗y2 = x2∗y1.

Let X be a finite set. Describe the equivalence relation having the greatest number of distinct...

Let X be a finite set. Describe the equivalence relation having the greatest number of distinct equivalence classes, and the one with the smallest number of equivalence classes.

select the relation that is an equivalence relation. THe domain set is (1,2,3,4). a. (1,4)(4,1),(2,2)(3,3) b....

select the relation that is an equivalence relation. THe domain set is (1,2,3,4). a. (1,4)(4,1),(2,2)(3,3) b. (1,4) (4,1)(1,3)(3,1)(2,2) c. (1,4)(4,1)(1,1)(2,2)(3,3)(4,4) d. (1,4)(4,1)(1,3)(3,1)(1,1)(2,2)(3,3)(4.4)

Prove that \strongly connected" is an equivalence relation on the vertex set of a directed graph

7. Prove that congruence modulo 10 is an equivalence relation on the set of integers. What...

7. Prove that congruence modulo 10 is an equivalence relation on the set of integers. What do the equivalence classes look like?

Let X be a non-empty set and R⊆X × X be an equivalence relation. Prove that...

Let X be a non-empty set and R⊆X × X be an equivalence relation. Prove that X / R is a partition of X.

2. Recall that the set Q of rational numbers consists of equivalence classes of elements of...

2. Recall that the set Q of rational numbers consists of equivalence classes of elements of Z × Z\{0} under the equivalence relation R defined by: (a, b)R(c, d) ⇐⇒ ad = bc. We write [a, b] for the equivalence class of the element (a, b). Using this setup, do the following problems: 2A. Show that the following definition of multiplication of elements of Q makes sense (i.e. is “well-defined”): [a, b] · [r, s] = [ar, bs]. (Recall this...

Describe the set of all unit tight frames with exactly ﬁve vectors, up to PRR-equivalence.

Set A = {1, 2, 3, 4}, write a binary relation R on A that is...

Set A = {1, 2, 3, 4}, write a binary relation R on A that is reflexive, symmetric and transitive, with (1, 2),(3, 2) ∈ R.

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