Assume A = R and the relation R ⊆ A × A such that for x,...

Assume A = R and the relation R ⊆ A × A such that for x, y, ∈ R, xRy if and only if sin2 x + cos2 y = 1. Prove that R is an equivalence relation and for any fixed x ∈ R, find the equivalence class x

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Colby Messinger answered 1 year ago

Let x be a set and let R be a relation on x such x is...

Let x be a set and let R be a relation on x such x is simultaneously reflexive, symmetric, and antisymmetric. Prove equivalence relation.

Let A = R x R, and let a relation S be defined as: “(x1, y1)...

Let A = R x R, and let a relation S be defined as: “(x1, y1) S (x2, y2) ⬄ points (x1, y1) and (x2, y2)are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you must give a counterexample.

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

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Consider the equation x^2+(y-2)^2 and the relation “(x, y) R (0, 2)”, where R is read...

Consider the equation x^2+(y-2)^2 and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “(x, y) belongs to the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation if, and only if, (x, y) R (0, 2)”. Does this equation determine a...

6. Let R be a relation on Z x Z such that for all ordered pairs...

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Question 1. Equivalence Relation 1 Define a relation R on by iff . Prove that R...

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Suppose x,y ∈ R and assume that x < y. Show that for all z ∈...

Suppose x,y ∈ R and assume that x < y. Show that for all z ∈ (x,y), there exists α ∈ (0,1) so that αx+(1−α)y = z. Now, also prove that a set X ⊆ R is convex if and only if the set X satisfies the property that for all x,y ∈ X, with x < y, for all z ∈ (x,y), z ∈ X.

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.

Assume a relation X(A,B,C) defined by the following statement: CREATE TABLE X (A int, B int,...

Assume a relation X(A,B,C) defined by the following statement: CREATE TABLE X (A int, B int, C int); The relation is currently empty. You have to insert exactly 3 tuples into the relation, without duplicates, to create a data instance in which the functional dependency A → BC holds and the functional dependencies B → C and C → B do not hold. Submit your 3 insert statements

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