Let R be the relation on Q defined by a/b R c/d iff ad=bc. Show that...

Let R be the relation on Q defined by a/b R c/d iff ad=bc. Show that R is an equivalence relation. Describe the elements of the equivalence class of 2/3.

Expert Solution

Colby Messinger answered 2 years ago

For the relation R(A,B,C,D,E) with the following Functional Dependencies: A → B, A → C, BC...

For the relation R(A,B,C,D,E) with the following Functional Dependencies: A → B, A → C, BC → D, AC → E, CE → A, list all non-trivial FDs following from the above. Generate all possible keys for R. Check whether R is in 3NF. If it is in 3NF, explain the criteria you used. If it is not in 3NF, convert it into 3NF, showing the new relations and their FDs.

2. Define a relation R on pairs of real numbers as follows: (a, b)R(c, d) iff...

2. Define a relation R on pairs of real numbers as follows: (a, b)R(c, d) iff either a < c or both a = c and b ≤ d. Is R a partial order? Why or why not? If R is a partial order, draw a diagram of some of its elements. 3. Define a relation R on integers as follows: mRn iff m + n is even. Is R a partial order? Why or why not? If R is...

Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if...

Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if and only if ad=bc. (a) Show that R is an equivalence relation. (b) What is the equivalence class of (1,2)? List out at least five elements of the equivalence class. (c) Give an interpretation of the equivalence classes for R. [Here, an interpretation is a description of the equivalence classes that is more meaningful than a mere repetition of the definition of R. Hint:...

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the...

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the diagraph for this relation b)show that R is an equivalence relation Part B: Now consider the relation R on A defined by aRb iff a divides b (Divides relation) c) Show that R is partial ordering d) Contruct the hasse diagram for this relation

Let a < c < b, and let f be defined on [a,b]. Show that f...

Let a < c < b, and let f be defined on [a,b]. Show that f ∈ R[a,b] if and only if f ∈ R[a, c] and f ∈ R[c, b]. Moreover, Integral a,b f = integral a,c f + integral c,b f .

Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.

The goal is to show that a nonempty subset C⊆R is closed iff there is a...

The goal is to show that a nonempty subset C⊆R is closed iff there is a continuous function g:R→R such that C=g−1(0). 1) Show the IF part. (Hint: explain why the inverse image of a closed set is closed.) 2) Show the ONLY IF part. (Hint: you may cite parts of Exercise 4.3.12 if needed.)

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

Question 1. Equivalence Relation 1 Define a relation R on by iff . Prove that R is an equivalence relation, that is, prove that it is reflexive, symmetric, and transitive. Determine the equivalence classes of this relation. What members are in the class [2]? How many members do the equivalence classes have? Do they all have the same number of members? How many equivalence classes are there? Question 2. Equivalence Relation 2 Consider the relation from last week defined as:...

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.

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a...

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a field

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