Question

suppose f is an integral element function on [0,1], p and q are partitions of [0,1]....

suppose f is an integral element function on [0,1], p and q are partitions of [0,1].

for any partitions A and B, let P = A U B. Then Up-Lp <= Ua-La.

is this statement true or false? either provide a proof or counterexample.

cross "element"

Homework Answers

Answer #1

Note : A U B = P implies we have more points in P than A. So for points x1 and x2 in A we can have x0 in between where x0 is in P. Thus adding more points decrease the upper sum as is clear from the above figures. And the opposite case holds for Lower sum. That is Increasing points in the partition makes the lower sum larger.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
suppose f is an integral element function on [0,1], p and q are partitions of [0,1]....
suppose f is an integral element function on [0,1], p and q are partitions of [0,1]. if Up-Lp <= Uq-La, then q belongs to p. is this statement true or false? either provide a proof or counterexample.
Suppose g: P → Q and f: Q → R where P = {1, 2, 3,...
Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4}, Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4, b)}. (a) Is Function f and g invertible? If yes find f −1 and    g −1 or if not why? (b) Find f o g and g o...
(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q) → ¬r...
(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...
For Problems #5 – #9, you willl either be asked to prove a statement or disprove...
For Problems #5 – #9, you willl either be asked to prove a statement or disprove a statement, or decide if a statement is true or false, then prove or disprove the statement. Prove statements using only the definitions. DO NOT use any set identities or any prior results whatsoever. Disprove false statements by giving counterexample and explaining precisely why your counterexample disproves the claim. ********************************************************************************************************* (5) (12pts) Consider the < relation defined on R as usual, where x <...
Suppose that Hannah and Sam have the production function         Q=F(L,K)Q=F(L,K)         Q=10L0.5K0.5.Q=10L0.5K0.5. The wage rate is $1,000...
Suppose that Hannah and Sam have the production function         Q=F(L,K)Q=F(L,K)         Q=10L0.5K0.5.Q=10L0.5K0.5. The wage rate is $1,000 per week and a unit of capital costs $4,000 per week. a. True or false? If we plot L along the horizontal axis and K along the vertical axis, then Hannah and Sam's output expansion path is a straight line that passes through the origin and has a slope of 0.25.      TrueFalse b. What is their cost function? Choose from the options below.     A:400QB:200Q2C:2,000Q0.5D:200Q+400Q2A: ...
Suppose the final goods production function is fixed-proportion, Q = f(E, L) = min{E,L}, where Q...
Suppose the final goods production function is fixed-proportion, Q = f(E, L) = min{E,L}, where Q is output level, E is energy input and L is the labor in- put. Let m be the marginal cost of energy per unit and w be the price of labor per unit. Suppose the demand function for final good is P = 1 - Q a). (10) Suppose energy and final good are produced by two different firms. Derive the cost function of...
Suppose the final goods production function is fixed-proportion, Q = f(E, L) = minf(E,L), where Q...
Suppose the final goods production function is fixed-proportion, Q = f(E, L) = minf(E,L), where Q is output level, E is energy input and L is the labor in- put. Let m be the marginal cost of energy per unit and w be the price of labor per unit. Suppose the demand function for final good is P = 1 - Q: a). (10) Suppose energy and nal good are produced by two different rm. Derive the cost function of...
Suppose that Hannah and Sam have the production function Q=F(L,K) Q=10L0.5K0.5. The wage rate is $1,000...
Suppose that Hannah and Sam have the production function Q=F(L,K) Q=10L0.5K0.5. The wage rate is $1,000 per week and a unit of capital costs $4,000 per week. a. True or false? If we plot L along the horizontal axis and K along the vertical axis, then Hannah and Sam's output expansion path is a straight line that passes through the origin and has a slope of 0.25. b. What is their cost function? Choose from the options below. A:400Q B:200Q^2...
1. Suppose the demand function for automobile industry is : Q = - 500 P +...
1. Suppose the demand function for automobile industry is : Q = - 500 P + 210 Px + 200 I + 20.000 POP + 1.000.000 i +600 A where Q : the number of new domestic automobiles demanded P : the average price of new domestic cars (in $), Px : the average price of luxury cars, I : disposable income per household (in $), POP : population i : average interest rate on car loans (in %), A...
True or False? No reasons needed. (e) Suppose β and γ are bases of F n...
True or False? No reasons needed. (e) Suppose β and γ are bases of F n and F m, respectively. Every m × n matrix A is equal to [T] γ β for some linear transformation T: F n → F m. (f) Recall that P(R) is the vector space of all polynomials with coefficients in R. If a linear transformation T: P(R) → P(R) is one-to-one, then T is also onto. (g) The vector spaces R 5 and P4(R)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT