Arrange the steps in the correct order to prove the theorem "If A and B are sets, A is uncountable, and A ⊆ B, then B is uncountable." Rank the options below.

a. Since A is a subset of B, taking the subsequence of {bn} that contains the terms that are in A gives a listing of the elements of A.
b. Thus B is not countable.
c. The elements of B can be listed as b1, b2, b3
d. Therefore A is countable, contradicting the hypothesis.

Answers

Answer 1

Answer:

Step-by-step explanation:

We are to rank the options given in the question to correctly prove the theorem that: "If A & B are set, and A is a subset of B"

To arrange the steps in the correct order, we have:

(a) Assume that B is countable

(b) The elements of B can be listed as b1, b2, b3

(c) Since A is a subset of B, taking the subsequence of {bn} that contains the terms that are in A gives a listing of the elements of A.

(d) Therefore A is countable, contradicting the hypothesis.

(e)  Thus B is not countable


Related Questions

many 2/3 are in 9/8?"

Answers

Answer:

1.6875   2/3's are in 9/8.

Step-by-step explanation:

(9/8)/(2/3)=1.6875

The volume of a suitcase if 8,556 cubic inches. It is 32 inches long and 15.5 inches high. What is width of the suitcase?

Answers

Answer:

17.25

Step-by-step explanation:

8556 / 32 / 15.5 = 17.25

There are 8 fish tanks in the pet shop. They just
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Answer:

27

Step-by-step explanation:

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hope it helps

Answer:

27

Step-by-step explanation:

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Answer:

type of music students prefer. How would the manager most likely get a random sample

that represents the school population?

Step-by-step explanation:

I may or may not have given my explanation in my answer 0.0

The coordinate point F(-8, 0) after a dilation with scale factor of 0.25, centered at the origin, becomes the point
O (-2,0)
O (-2, 0.25)
O (2, 0.25)
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Answers

Answer:

[tex](-2,\, 0)[/tex].

Step-by-step explanation:

Dilate a point [tex](x,\, y)[/tex] by a scale factor of [tex]r[/tex] with [tex](a,\, b)[/tex] as the center, and the resultant point would be at [tex](a + r\, (x - a),\, b + r\, (y - a))[/tex].

In this question:

Point to dilate: [tex](x,\, y) = (-8,\, 0)[/tex].

Scale factor: [tex]r = 0.25[/tex].

Center of dilation: [tex](a,\, b) = (0,\, 0)[/tex].

The resultant point would be:

[tex](0 + 0.25\, (-8 - 0),\, 0 + 0.25\, (0 - 0))[/tex], which simplifies to [tex](-2,\, 0)[/tex].

Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b. (Remember that all the way around a circle is 360°. Start by finding the measure of angle a in the figure on the left.)

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Answer:

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Step-by-step explanation:

have a great day

what is the key idea of this passage ​

Answers

You have to insert the passage first

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change 3 to a fraction
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multiply by the reciprocal (flip 3/1 around)
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Answer:

I hope this helps you

Step-by-step explanation:

1/8 ÷ 3 = 1/8 × 1/3

= 1/24

= 0.0416666667

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The answer is d>3

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Answer:

second option.

Step-by-step explanation:

mark me as brainliest plz

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Answers

8 I think I hope you get this right

Answer:

I think its 16

Step-by-step explanation:

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Answers

Answer:

x= 11/3

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Step-by-step explanation:

-8x+y=-16

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Multiply the second equation by -1, we get,

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--------------------

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x=11/3. so,

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Gold is mined at Cortez Gold Mine in Nevada. For every ton of raw material dug out of the ground, you get one ounce of gold. Each truck hauls 394 tons, and each day, there are 1000 trucks that haul material out of the ground. Assuming the current price of gold to be $1,607 per ounce. How much money is made each day at Cortez Gold Mine

Answers

Answer:

[tex]\$633158000[/tex]

Step-by-step explanation:

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There are 1000 trucks so

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

100 on quiz Edge 2021

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Step-by-step explanation:

Answer:

5/6 × 4 = ?

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

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