Match the following: Let X = {1,2,3,4}, Classify the relations of X on X ___ {(1,4),(1,2)}...

Match the following:

Let X = {1,2,3,4}, Classify the relations of X on X
___ {(1,4),(1,2)}
___{ (1,4),(4,1),(2,3) }
___{ (1,4),(4,4),(2,3),(3,3)}
___{ (1,1),(4,4),(2,2),(3,3) }

a. Is a function
b. Is a relation
c. Is transitive
d. Is a relation of equivalence
e. Is not a function

Expert Solution

Colby Messinger answered 2 years ago

Let R and S be equivalence relations on a set X. Which of the following are...

Let R and S be equivalence relations on a set X. Which of the following are necessarily equivalence relations? (1)R ∩ S (2)R \ S . Please show me the proof. Thanks!

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by...

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by (a,b)R(c,d) iff ad = bc Write out each equivalence class (by "write out" I mean tell me explicitly which elements of A are in each equivalence class) Hint: |A| = 16 and there are 11 equivalence classes, so there are several equivalence classes that consist of a single element of A.

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)

Consider a toy population that consists of three numbers 1,2, and 3. A. Let X be...

Consider a toy population that consists of three numbers 1,2, and 3. A. Let X be the randomly selected number (P(X = x) = 1/3) for x = 1,2,3. Find E(X) and V(X). B. What are the values of the population mean µ and population variance σ^2? C. Take a random sample of size n = 2 (with replacement). Determine the sampling distribution of the sample mean x̄, i.e. find the probability for each possible value of x̄. D. Find...

Let S be the set of all integers x ∈ {1,2,...,100} such that the decimal representation...

Let S be the set of all integers x ∈ {1,2,...,100} such that the decimal representation of x does not contain the digit 4. (The decimal representation does not have leading zeros.) • Determine the size of the set S without using the Complement Rule. • Use the Complement Rule to determine the size of the set S. (You do not get marks if you write out all numbers from 1 to 100 and mark those that belong to the...

2. Let A = {1,2,3,4}. Let F be the set of all functions from A to...

2. Let A = {1,2,3,4}. Let F be the set of all functions from A to A. Recall that IA ∈ F is the identity function on A given by IA(x) = x for all x ∈ A. Consider the function E : F → A given by E(f) = f(1) for all f ∈ F. (a) Is the function E one-to-one? Prove your answer. (b) Is the function E onto? Prove your answer. (c) How many functions f ∈...

Match the following questions with 1,2 or 3 insulin and glucagon ? hormones can activate metabolism...

Match the following questions with 1,2 or 3 insulin and glucagon ? hormones can activate metabolism through? How is glycolysis regulated? 1.phosphorylation, gene expression/protein degradation, enzyme localization 2.These hormines dictate whether glucose flows through glycolysis or gluconeogenesis 3.Low Blood Glucose -----> increase glucagon: Phosphorylation of bifunctional enzyme: --inactive PFK2, active FBPase2 --decrease F-2,6-BP --decrease PFK1 activity ; Phosphorylation of pyruvate kinase --decrease pyruvate kinase activity

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and...

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and y=1,2 calculate the covariance of x and y calculate the correlation coefficient of x and y Thank you

Calculate each of the following (or indicate why it is not defined) (a) (1,2,3,4) x (4,3,2,1)...

Calculate each of the following (or indicate why it is not defined) (a) (1,2,3,4) x (4,3,2,1) (b) (1,1,1) x [(1,2,3) x (3,3,0)] (C) (1,1,1). [(1,2,3) x (3,3,0) (d) (1,1,1) x [(1,2,3). (3,3,0)] (e) (1,1,1) x [(1,2,3) - (3,3,0)] (f) (1,1,1) + [(1,2,3) X (3,3,0)]

Let S(n) be the number of subsets of {1,2,...,n} having the following property: there are no...

Let S(n) be the number of subsets of {1,2,...,n} having the following property: there are no three elements in the subset that are consecutive integers. Find a recurrence for S(n) and explain in words why S(n) satisfies this recurrence

Question