Question

In: Advanced Math

Let A = R x R, and let a relation S be defined as: “(x​1,​ y​1)​...

  1. Let A = R x R, and let a relation S be defined as: “(x​1,​ y​1)​ S (x​2,​ y​2)​ ⬄ points (x​1,​ y​1)​ and (x​2,​ y​2)​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.

Solutions

Expert Solution

Colby Messinger answered 1 year ago
Next > < Previous

Related Solutions

Let S = {2 k : k ∈ Z}. Let R be a relation defined on...
Let S = {2 k : k ∈ Z}. Let R be a relation defined on Q− {0} by x R y if x y ∈ S. Prove that R is an equivalence relation. Determine the equivalence class
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 x, y ∈ R \ {0}. Prove that if x < x^(−1) < y...
. Let x, y ∈ R \ {0}. Prove that if x < x^(−1) < y < y^(−1) then x < −1.
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.
1. Let U = {r, s, t, u, v, w, x, y, z}, D = {s,...
1. Let U = {r, s, t, u, v, w, x, y, z}, D = {s, t, u, v, w}, E = {v, w, x}, and F = {t, u}. Use roster notation to list the elements of D ∩ E. a. {v, w} b. {r, s, t, u, v, w, x, y, z} c. {s, t, u} d. {s, t, u, v, w, x, y, z} 2. Let U = {r, s, t, u, v, w, x, y, z},...
6. (a) let f : R → R be a function defined by f(x) = x...
6. (a) let f : R → R be a function defined by f(x) = x + 4 if x ≤ 1 ax + b if 1 < x ≤ 3 3x x 8 if x > 3 Find the values of a and b that makes f(x) continuous on R. [10 marks] (b) Find the derivative of f(x) = tann 1 1 ∞x 1 + x . [15 marks] (c) Find f 0 (x) using logarithmic differentiation, where f(x)...
let R be a region bounded by x = 0 and x =1 and y =...
let R be a region bounded by x = 0 and x =1 and y = 0 and y = 1. Suppose the density is given by 1/y+1.Notice that R is denser near the x axis. As a result we might expect the centre of mass to be below the geometric center(1/2,1/2). Also since the density does not depend on x we do expect moment of inertia about the x axis to be 1/2. verify the moment of inertia about...
Let S = {-3, -2, -1, 0, 1, 2, 3}. Define a relation R on S...
Let S = {-3, -2, -1, 0, 1, 2, 3}. Define a relation R on S by: xRy if and only if x = y + 4n for some integer n. a) Prove that R is an equivalence relation. b) Find all the distinct equivalence classes of R.
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT