Let X, Y be sets and f : X Y. Prove that the following are equivalent.

Question:

Let X, Y be sets and f : X → Y. Prove that the following are equivalent.
a) f is 1-1 on X.
b) f(A\B) = f(A)\f(B) for all subsets A and B of X.
c) f-1(f(E)) = E for all subsets £ of X.
d) F(A ∩ B) = f(A) ∩ f(B) for all subsets A and B of X.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 03:54 AM

See More Questions

Prove that the following formulas hold for all n N. a) b) c) d) n(n1) k-n(n + 1 )(2n + 1) 6 !
Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if x + y = 0.
Let A and B be orthogonally diagonalizable n ( n matrices and let c be a scalar. Use the Spectral Theorem to prove that the following matrices are orthogonally diagonalizable: (a) A + B (b) cA (c) A2
Refer to the Webers Data Set above. 1. Compute the direct materials efficiency variance for onion, mustard, and ketchup. 2. As a manager, what would you learn from the variances and supporting data?...
Cox Media Corporation pays an 11 percent coupon rate on debentures that are due in 10 years. The current yield to maturity on bonds of similar risk is 8 percent. The bonds are currently callable at...
Which of the following is not a step in the accounting process? a. Identification b. Auditing c. Recording d. Communication
You have collected the following data: If you place these five numbers in a bag and randomly select one, what is the probability the number (X) will be ... a. equal to 6 ? b. less than 11 ? c....
You are a pricing analyst for QuantCrunch Corporation, a company that recently spent $ 15,000 to develop a statistical software package. To date, you only have one client. A recent internal study...
Discuss the concepts of mean, median, mode, and standard deviation. Include when each should be used and evaluate the differences of each.
You have identified relevant controls for several assertions within the revenue cycle, and you must use IDEA to perform several tests of controls. Required: a. ELM has a policy of using pre numbered...
Let f(x) = x2. a) Find subsets B and C of R such that f(C\B) f(C)\f(B). b) Find a subset E of R such that f-1(f(E)) E.
Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones. a) Suppose that E is a set. If there exists a function f from E...
Evaluate the following integral using the trapezoidal rule, and calculate the difference between analytical and numerical solutions: \[ \begin{equation*} I=\int_{0}^{10}\left(x^{2}+2 x+5ight) d x...
How do you think the following races are positioned: Boston Marathon, Run Like Hell 5k Halloween Race, and the Bowling Green 10k Classic? Draw a two- dimensional perceptual map to illustrate the...
Describe the main issues that arise when conducting historical analysis of real estate returns.
Identify risks faced by investors in emerging market equities over and above those that are faced by fixed-income investors in such markets.
A client has asked his adviser to explain the key considerations in forecasting exchange rates. The advisers firm uses two broad complementary approaches when setting expectations for exchange rate...
Given the Martins risk and tax preferences, the taxable portfolio should be rebalanced: A. less often than the tax-deferred portfolio. B. as often as the tax-deferred portfolio. C. more often than...
Describe the four enhancing qualitative characteristics of financial information.
An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the childs...
Prove that if f: Rn Rm is differentiable at a Rn, then it is continuous at a.
A function f: R2 R is said to be independent of the second variable if for each x R we have f (x, y1) = f (x, y2) for all y1, y2. R Show that f is independent of the second variable if and only if...
Define when a function f: Rn R is independent of the first variable and find f1 (a, b) for such f. Which functions are independent of the first variable and also of the second variable?
How truly do drive elements and social impact instruments, for example, social personality hypothesis and gathering polarization, deeply mold hierarchical way of behaving and decision-production at...
Sub Station and Planet Sub reported the following selected financial data ( $ in thousands ) . Sub Station s business strategy is to sell the best tasting sandwich with the highest quality...
The credit manager of Montour Fuel has gathered the following information about the company's accounts receivable and credit losses during the current year: Net credit sales for the year $ 7 , 5 0 0...

Let X, Y be sets and f : X Y. Prove that the following are equivalent.

Question:

Step by Step Answer:

a implies b By definition fAB fAfB holds whether f is 11 or not To prove t...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions