Question: Suppose that A and B are sets and that B is uncountable. If there exists a function which takes A onto B, prove that A

Suppose that A and B are sets and that B is uncountable. If there exists a function which takes A onto B, prove that A is uncountable.

Step by Step Solution

★★★★★

3.33 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let g be a function that takes A onto B If A is ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (165).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

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...

Q:

Suppose that A and B are similar matrices. Prove that A3 and B3 are similar matrices. Generalize.

Q:

1. What is the relationship between the two sets A and B if A B = ? 2. What is the relationship between the two sets A and B if n (A B) = n (A) + n (B)? 3. Suppose that A and B are subsets of the...

Q:

Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones. a) Let f(x) = sin x. Then the function is a bijection, and its...

Q:

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Q:

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

Q:

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

What typically determines the process that a firm uses to create its product?

Q:

Write the sum in sigma notation 5 + 8 + 11 + 14 +...+ 95 A B i 1 A= 95 B= n Question 7 one. Hint: The answer for A should be a number and the answer for B should be an expression. Question Help:...

Q:

The main functions of a futures exchange ( either as an independent body or a division or a futures exchange ) is to do the following for futures trading: a . Tracking, Margin call, trading b ....

Q:

(Technological Change and Unemployment) What are some examples, other than those given in the chapter, of technological change that has caused unemployment? And what are some examples of new...

Q:

2. Prove that each of the following inequalities. (a) VI + 2x O. (b) log x ::; x-I for all x ::::: 1. (c) 7(x-l)

Q:

1. Evaluate the following limits. (a) (b) (c) (d) (e) 1. sin(3x) 1m . x--+O X r cos x - eX x!..W+ log(1 + x2 ) . (X) l/x2 hm -- x--+O sin x lim xx. x--+O+ 1. log x x-1-+m 1 S.I n ( 7rX ) (f) }!.ll!,...

Q:

9. Consider the following outline to a proof of the Chain Rule for real functions. Let y = f(x), Yo = f(xo), and observe that y ~ Yo as x ~ Xo. Thus lim go f(x) - 9 0 f(xo) = lim g(f(x)) - g(f(xo))...

Q:

XYZ Company has expected earnings of $3.00 for next year and usually retains 40 percent for future growth. Its dividends arc expected to grow at a rate of 10 percent indefinitely. If an investor has...

Q:

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .18 .353 .453 .333 Good .42 .123 .103 .173 Poor .32...

Q:

Which of the following is TRUE about IRR? 1. The IRR rule accounts for the risk of the cash flows. II. When the cash flows change sign more than once, there is more than one IRR. I only Neither I nor...