Homework Statement
Find the length of the curve
x = 3 y^{4/3}-\frac{3}{32}y^{2/3}, \quad -64\le y\le 64
Homework Equations
Integral for arc length (L):
L = \int_a^b \sqrt{1 + (\frac{dy}{dx})^{2}} dx
The Attempt at a Solution
Using symmetry of the interval and the above integral for arc...
Homework Statement
Find a basis for the subset S = {(1, 2, 1), (2, 1, 3), (1, -4, 3)}
Homework Equations
The Attempt at a Solution
I'm not absolutely sure I'm doing this correctly but here is my attempt:
First, I put the vectors in S in the rows of a matrix (using multiple...
Homework Statement
How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1}
a) that are one-to-one?
b) that assign 0 to both 1 and n?
c) that assign 1 to exactly one of the positive integers less than n?
Homework Equations...
Hello everyone,
For homework my instructor assigned problem from the book. To show which problems to do she wrote this: 4n + 1 N={1, 2, 3...}. Does this mean problems 5, 9, 13, . . . ?
Thanks for any suggestions.
Homework Statement
Let S = {2,3,4,5} and consider the poset (S, <=) where <= is the divisibility relation. Which of the following is true?
1. 3 is a minimal element
2. 4 is a greatest element
3. 2 is a least element
4. Both 2 and 3
Homework Equations
The Attempt at a Solution
My answer...
Homework Statement
Could someone help with this problem?
Determine which of the following posets (S, <=) are lattices.
1. A = {1, 3, 6, 9, 12} and <= is the divisibility relation.
2. B = {1, 2, 3, 4, 5} and <= is the divisibility relation.
3. C = {1, 5, 25, 100} and <= is the...
Homework Statement
Are the following subsets partitions of the set of integers?
The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4.
Homework Equations
The Attempt at a Solution
Yes, it is a partition of the set of integers...
Homework Statement
Given the graph, determine if the following sequences form a walk, path and/or a circuit.
http://img843.imageshack.us/img843/5686/digraph.png [Broken]
1. a, b, c, e
2. b, c, d, d, e, c, f
3. a, b, c, f, g, a
4. b, c, d, e
Homework Equations
The Attempt at a Solution
1...
Homework Statement
Find the matrix that represents the given relation. Use elements in the order given to determine rows and columns of the matrix.
R on {2, 3, 4, 6, 8, 9, 12} where aRb means a|b.
Homework Equations
The Attempt at a Solution
1 0 1 1 1 0 1
0 1 0 1 0 1 1
0 0...
Homework Statement
2. Let R1 = {(1,1),(1,2),(2,3),(3.4), (2,4) } and
R2 = {(1,1),(2,2),(2,3),(3,3),(3,4) } be relations from {1,2,3} to {1,2,3,4}
R1⨁ R2
Homework Equations
The Attempt at a Solution
R1⨁ R2 = {(1,2), (2,2), (2, 4), (3,3)}
Is this correct?
Homework Statement
Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.
The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}
Homework Equations
The Attempt at a Solution
Not reflexive because there is...
Homework Statement
Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.
The relation R on all integers where aRy is |a-b|<=3
Homework Equations
The Attempt at a Solution
The relationship is reflexive because any number minus itself will be...
Homework Statement
Suppose that if there are at least 2 people in a room and each person in the room shakes hands with everyone else, but not with himself. Show that the number of handshakes is (n^2-n)/2.
Make sure to show P(1), P(k) and prove P(k+1)
Homework Equations
The...
Homework Statement
What is the greatest common divisor and least common multiple of the integers below (answer should be left in exponential form)?
2^{3}, 3^{3}, 5^{1}, 11^{2}, 13^{3} and 2^{1}3^{3}5^{2}7^{4}13^{1}
Homework Equations
The Attempt at a Solution
This is exactly the way the...
Homework Statement
Show that the binary expansion of a positive integer can be obtained form its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.
Homework Equations
The Attempt at a Solution
I know that this is true but I have no...
Homework Statement
To establish a big - O relationship, find witnesses C and k such that |f(x)| <= C|g(x)| whenever x > k.
Show that x^3 is O(x^4) but that x^4 is not O(x^3).
Homework Equations
If f(x) is O(g(x)) then there is a C such that f(x) <= Cg(x).
The Attempt at a...
Homework Statement
How many comparisons does the insertion sort use to sort the list n, n-1, ......2, 1?
Homework Equations
The Attempt at a Solution
Insertion sort compares every element with every other element in the list, but I'm unsure what this question is asking. Why does...
Homework Statement
Let A = {1, 2}, B = {3, 4}, C = {3}
What is (A x B) - (B x C)?
Homework Equations
The Attempt at a Solution
(A x B) - (B x C) = {(1, 3), (1, 4), (2, 3), (2, 4)} - {(3, 3), (4, 3)}
= {(1, 3), (1, 4), (2, 3), (2, 4)}
Since there where no elements in (B x...
Homework Statement
Is the function one-to-one, onto, both, or neither?
f: Z→Z has the rule of f(n) = 4n^3 - 1
Homework Equations
The Attempt at a Solution
My answer: one-to-one
Is this correct?
Homework Statement
Find a formula that generates the sequence:
2/(3 x 4), -3/(4 x 5), 4/(5 x 6), -5/(6 x 7), . . .
Homework Equations
The Attempt at a Solution
Here is what I have so far:
a_n = -1(n/((n + 1)(n + 2)))
Now, I'm stuck. The formula generates a negative number every time. I...
Homework Statement
Find the sum of the sequence:
2, -2/3, 2/9, -2/27, 2/81, . . .
Homework Equations
The Attempt at a Solution
I can see that the number is multiplied by -1/3, but I'm unsure of how to find the sum.
Any pointers?
Homework Statement
Note: [x] denotes the floor of x.
Prove that [3x] = [x] + [x + 1/3] + [x + 2/3]
Homework Equations
The Attempt at a Solution
Let x = n + E, where n is an integer and 0≤ E < 1. We have three cases:
Case 1: 0 ≤ E < 1/3
3x = 3n + 3E and [3x] = 3n, since 0...
Homework Statement
Suppose f : R→R and g : R→R where g(x) = 3x + 5 and g o f(x) = x^2 - 7.
Find the rule for f.
Homework Equations
The Attempt at a Solution
These seem pretty simple, but I want to make sure I'm on the right track.
3(f(x)) + 5 = x^2 - 7
3(f(x)) = x^2 - 12
f(x) = (x^2 -...
Homework Statement
Let g : A → B and f : B → C where A = {a,b,c,d}, B = {1,2,3}, C = {2,3,6,8}, and g and f are defined by g = {(a,2),(b,1),(c,3),(d,2)} and f = {(1,8),(2,3),(3,2)}.
Find f o f
Homework Equations
The Attempt at a Solution
I know how to find f o g by working...
To me this problem doesn't seem right. Here it is:
Is the following function one-to-one, onto, both, or neither?
f: R→N f(x) = ceiling 2x/3
My answer: onto
Although, wouldn't this function be invalid since it produces negative numbers and the set of natural numbers doesn't include...
Hello all,
This is tripping me up a bit an I just want to see if I on the right track. Here is the problem:
Give a function from Z to N that is onto N but not one-to-one.
Answer: f(x) = {x if x ≥ 0, -1x if x < 0
Seems simple, but I think it works. Note: in our book, 0 is included in...
Hello everyone,
I just want to make sure I'm doing these problems correctly. Here they are
Are the following functions?
1. F : Z→Z where F(x) = 4/7x + 1
Answer: Not a function. F(1) is not an integer.
2. G : R→R where G(x) = {2x + 2 if x ≥ 0, x - 3 if x ≤ 0
Answer: Not a function...
Here's the problem:
Suppose U = {x | -10 ≤ x ≤ 10 and x ∈ Z}, A = all multiples of 2, B = all multiples of 3, and C = {-10, -9, -8, -6, -4, 0, 1, 3, 5, 6, 8, 10}.
Find C - (A-B).
Solution:
A = {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}
B = {-9, -6, -3, 0, 3, 6, 9}
C = {-10, -9, -8, -6, -4, 0, 1...
While practicing power set problems I came across one that has me stumped.
The problem asks: Is the following set is a power set of of a set?
{∅, {b, ∅}, {a}, {a, b}, {b}}
My answer: This set has 5 elements. Since 5 is not a power of 2, this cannot be the power set of any set.
The...