Question

Exercise 3.5.6: Roster notation for sets defined using set builder notation and the Cartesian product.

Express the following sets using the roster method. Express the elements as strings, not n-tuples.

**QUESTION A and B already answered. Please provide
solutions for C,D,E using same method, and show some explantion how
you got answer.**

(a)

{0x: x ∈ {0, 1}^{2}}

answer: { 000, 001, 010, 011 }

(b)

{0, 1}^{0} ∪ {0, 1}^{1} ∪ {0, 1}^{2}

answer : { λ, 0, 1, 00, 01, 10, 11 }

(c)

{0x: x ∈ B}, where B = {0, 1}^{0} ∪ {0, 1}^{1} ∪
{0, 1}^{2}.

(d)

{xy: where x ∈ {0} ∪ {0}^{2} and y ∈ {1} ∪
{1}^{2}}

(e)

{xy: x ∈ {aa, ab} and y ∈ {a} ∪ {a}^{2}}

Answer #1

Express the range of each function using roster notation.
Let A = {1, 2, 3}.
f: A × A → Z×Z, where f(x,y) =
(x,y+1).

1. Use the roster method to describe the elements of the
following set.
x∈ℤ||x−3|<12 and x is a multiple of 3
2. Use the roster method to describe the elements of the
following set.
{n∈ℕ∣∣∣1n+6⩾6272 and n is a multiple of 5}
3. Determine the cardinality of the following sets.
{x∈ℤ|−4⩽x⩽3}:
{x∈ℕ|−4⩽x⩽3}:
4. Evaluate the following expressions. [Hint: start by factoring
the polynomial.]
∣∣{x∈ℚ∣∣18x3+69x2+56x=0}∣∣=
∣∣{x∈(0,∞)∣∣18x3+69x2+56x=0}∣∣=
∣∣{x∈ℤ∣∣18x3+69x2+56x=0}∣∣=
5. Evaluate the following expressions. [Hint: start
by factoring the polynomial.]
∣∣{x∈ℝ∣∣x4+11x2+28=0}∣∣=
∣∣{x∈ℚ∣∣x4+11x2+28=0}∣∣=
∣∣{x∈ℕ∣∣x4+11x2+28=0}∣∣=
6....

1.express dw/dt as a function of t, both by using the Chain Rule
and by expressing w in terms of t and differentiating directly with
respect to t. Then evaluate dw/dt at the given value of t.
a)w= -6x^2-10x^2 , x=cos t,y=sint, t=pi/4
b)w=4x^2y-4y^2x, x=cost y=sint, --> express n terms of t
2.Find the linearization L(x,y) of the function (x,y)=e^x
cos(9y) at points (0,0) and (0,pi/2)

(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q)
→ ¬r are logically equivalent using either a truth table or laws of
logic.
(2) Let A, B and C be sets. If a is the proposition “x ∈ A”, b
is the proposition “x ∈ B” and
c is the proposition “x ∈ C”, write down a proposition involving a,
b and c that is logically equivalentto“x∈A∪(B−C)”.
(3) Consider the statement ∀x∃y¬P(x,y). Write down a...

10.16: Write a user-defined MATLAB function that solves a
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argument ODE is a name for the function that calculates dy/dx. It
is a dummy name for the function that is imported into odeMIDPOINT.
The arguments a and b define the domain of the solution, h is step
size; yINI is initial value. The output arguments, x...

Using these sets
Numerals = {0, 1, 2, 3, 4,5}
Letters = {a, b, c, u, x, y, z}
Symbols = {@, #, $, %, ^, &}
Compute the number of passwords for the
following:
a) Passwords of length 5 that may include numerals, letters, and
symbols but must start with a symbol and have no repeated
characters.
b) Passwords of length 3, 4, or 5 that may have numerals or
symbols and have no repeated characters.
c) Passwords of...

In a small-scale regression study, we collected data on the
number of children in a family Xi and the number of
hours per week spent shopping Yi. The following data
were obtained:
i
1
2
3
4
5
6
Xi
2
6
3
1
1
9
Yi
13
17
12
12
9
22
Assume we performed a simple linear regression of Yi
on Xi, i.e. E(Yi) = ?0 +
?1Xi
(a) By hand compute X?X, X?Y, (X?X)-1, b,
Y^(means Y-hat),...

For each of the following four problems:
a) Draw a free-body diagram, using the notation we developed in
class
b) Using only variables, write Newton’s second law for the
x-axis and the y-axis
c) Solve algebraically for the quantities asked for using the
information given in the
statement of the problem
d) Calculate a numerical answer by entering the values given
into the expressions found
For problem 1, use standard axes (+x to the right and +y
upwards). For problem...

The net force on a current loop in a uniform magnetic
field is zero. But what if B? is not
uniform? The figure (Figure 1) shows a square loop of wire that
lies in the xy-plane. The loop has corners at
(0,0),(0,L),(L,0), and (L,L)
and carries a constant current I in the clockwise
direction. The magnetic field has no x-component but has
both y- and z-components: B?
=(B0z/L)j^+(B0y/L)k^,
where B0 is a positive constant.
Part G
Find the magnitude of the...

Calculate two iterations of Newton's Method to approximate a
zero of the function using the given initial guess. (Round your
answers to three decimal places.)
45. f(x) = x5 −
5, x1 = 1.4
n
xn
f(xn)
f '(xn)
f(xn)
f '(xn)
xn −
f(xn)
f '(xn)
1
2
40. Find two positive numbers satisfying the given
requirements.
The product is 234 and the sum is a minimum.
smaller value=
larger value=
30.Determine the open intervals on which the graph is...

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