For each of the following relations, determine if f is • a function, • surjective, or...

For each of the following relations, determine if f is
• a function,
• surjective, or
• injective.
Conclude by stating if the relation represents a bijective function.
For each point, state your reasoning in proper sentences.
a) f = {(a, b) ∈ N
2 × N | a ∈ N
2
, a = (a1, a2), b, a1, a2 ∈ N, b = a1a2}
b) f = {(x, y) ∈ S
2
| y = x
2}, where S = {x ∈ R | x ≥ 0}

Expert Solution

Colby Messinger answered 2 years ago

3. For each of the following relations on the set Z of integers, determine if it...

3. For each of the following relations on the set Z of integers, determine if it is reflexive, symmetric, antisymmetric, or transitive. On the basis of these properties, state whether or not it is an equivalence relation or a partial order. (a) R = {(a, b) ∈ Z 2 ∶ a 2 = b 2 }. (b) S = {(a, b) ∈ Z 2 ∶ ∣a − b∣ ≤ 1}.

Determine whether each of these proposed definitions is a valid recursive definition of a function f...

Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f (n) when n is a nonnegative integer and prove that your formula is valid. e) f (0) = 2, f (n) = f (n − 1) if n is odd and n ≥ 1 and f (n) = 2f (n − 2) if...

Determine whether each of these proposed definitions is a valid recursive definition of a function f...

Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid. a) f(0) = 1, f(n) = -f(n-1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f(2) = 2, (n) = f(n-3) for n ≥ 3. c) f(0)...

1. expand each function in a Taylor Series and determine radius of convergence. a) f(x) =...

1. expand each function in a Taylor Series and determine radius of convergence. a) f(x) = 1/(1-x) at x0 = 0 b) f(x) = e^(-x) at x0 = ln(2) c) f(x) = sqrt(1+x) at x0 = 0

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = log2 (x)

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = log2 (x)

Consider the function f(x) = x 4 − 4x 2 . Determine the following: • The...

Consider the function f(x) = x 4 − 4x 2 . Determine the following: • The (x,y) coordinate pairs of the local minima and local maxima. • The (x,y) coordinate pair of the absolute minimum and absolute maximum, should they exist. If the absolute min/max is obtained at multiple points, list all of them. • The intervals of increasing and decreasing. • The intervals of concavity. That is, explain exactly where this function is convex and exactly where this function...

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.

Find the Green's function for each of the following problem, and determine the solution of each...

Find the Green's function for each of the following problem, and determine the solution of each of the following boundary-value problem: y" + 4y = e^x y(0) = 0 y'(1) = 0

Let A = {1,2,3}. Determine all the equivalence relations R on A. For each of these,...

Let A = {1,2,3}. Determine all the equivalence relations R on A. For each of these, list all ordered pairs in the relation.

Question

For each of the following relations, determine if f is • a function, • surjective, or...

Solutions

Expert Solution

Related Solutions

3. For each of the following relations on the set Z of integers, determine if it...

Determine whether each of these proposed definitions is a valid recursive definition of a function f...

Determine whether each of these proposed definitions is a valid recursive definition of a function f...

1. expand each function in a Taylor Series and determine radius of convergence. a) f(x) =...

For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = log2 (x)

Consider the function f(x) = x 4 − 4x 2 . Determine the following: • The...

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.

For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.

Find the Green's function for each of the following problem, and determine the solution of each...

Let A = {1,2,3}. Determine all the equivalence relations R on A. For each of these,...