1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wlad13 [49]
3 years ago
6

Decide which of the following represent true statements about the nature of set. For any that are false, provide a specific exam

ple where the statement in question does not hold.
(a) If A1 ⊇ A2 ⊇ A3 ⊇ A4 ... are all sets containing an infinite number of elements, then the intersection n-1 An is infinite as well.
Mathematics
1 answer:
mart [117]3 years ago
8 0

Answer:

If the intersection is finite the statement  is true, but if the intersection is infinite the statement is false.

Step-by-step explanation:

From the statement of the problem I am not sure if the intersection is finite or infinite. Then, I will study both cases.

Let us consider first the finite case: A = \cap_{i=1}^{n}A_i. Because the condition A1 ⊇ A2 ⊇ A3 ⊇ A4 ... we can deduce that the set A_n is a subset of each set A_i with i\leq n. Thus,

\cap_{i=1}^{n}A_i = A_n.

Therefore, as A_n is infinite, the intersection is infinite.

Now, if we consider the infinite intersection, i.e. A = \cap_{k=1}^{\infty}A_k the reasoning is slightly different. Take the sets

A_k = (0,1/k) (this is, the open interval between 0 and 1/k.)

Notice that (0,1) ⊇ (0,1/2) ⊇ (0, 1/3) ⊇(0,1/4) ⊇...So, the hypothesis of the problem are fulfilled. But,

\cap_{k=1}^{\infty}(0,1/k) = \empyset

In order to prove the above statement, choose a real number x between 0 and 1. Notice that, no matter how small x is, there is a natural number K such that 1/K. Then, the number x is not in any interval (0,1/k) with k>K. Therefore, x is not in the set [tex]\cap_{k=1}^{\infty}(0,1/k)[\tex].

You might be interested in
How many points determine a unique line?
Nesterboy [21]
B. 2 Points determine a unique line
4 0
3 years ago
Read 2 more answers
Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time he will use the Same amount of plan
DanielleElmas [232]

Answer:

3 7/12 kg

He doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time

Step-by-step explanation:

On sunday , sheldon bought 4 1/2 kg of plant food. He uses 1 2/3 kg on his strawberry plants and used 1/4 kg for his tomato plants. b. Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time. He will use the same amounts of plant food as before. How much plant food will be need? Does he have enough left to do so.

Total plant bought = 4 1/2 kg

Strawberry = 1 2/3 kg

Tomato = 1/4 kg

Strawberry + tomato

= 1 2/3 + 1/4

= 5/3 + 1/4

= 20+3/12

= 23/12 kg

Total remaining after Sunday

= Total - used

= 4 1/2 - 23/12

= 9/2 - 23/12

= 54-23/12

= 31/12

= 2 7/12 kg

Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time.

Strawberry = 2 × 1 2/3

= 2 × 5/3

= 10/3 kg

Tomato = 1 × 1/4

= 1/4 kg

Total plant needed to feed strawberry two more times and tomato 1 more time

= 10/3 kg + 1/4 kg

= 40+3/12

= 43/12 kg

= 3 7/12 kg

He will need 3 7/12 kg of plant

He doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time

3 0
3 years ago
Simplify 2x – 9y + 4x + 11y by combining like terms and then evaluate at x = -2<br> and y = 4.
Mashcka [7]

Step-by-step explanation:

= 2x - 9y + 4x + 11y

First of all combining like terms

So

= 2x + 4x - 9y + 11y

= 6x + 2y

Now putting values

= 6 (-2) + 2(4)

= - 12 + 8

= - 4

7 0
3 years ago
I need help, the solid below is made from cubes find it volume
Art [367]

Answer:

[tex]\purple{\rule{45pt}{7pt}}\purple{\rule{45pt}{999999pt}}[tex]

5 0
2 years ago
Read 2 more answers
A hardware store owner is replenishing his stock of base paint for an upcoming home improvement sale. He conducted a survey to d
antiseptic1488 [7]

Solution:

                       Matte Satin    Glossy Total

Homeowners 0.08 0.20 0.24 0.52

Contractors 0.04 0.26 0.18         0.48

Total         0.12         0.46 0.42   1

Approximately what percentage of contractors prefer the glossy finish?

Answer: Percentage of contractors who prefer the glossy finish is:

\frac{0.18}{0.48}=0.375&#10; or 37.5\%

Therefore, the option D. 37.5% is correct

6 0
3 years ago
Read 2 more answers
Other questions:
  • Choose the correct answer. If one balloon is larger than another, it has a greater _________________.
    9·2 answers
  • What is the square root of -1?
    6·1 answer
  • 2. Graph each equation using a table of values.<br> (a)) y = 3x - 1
    5·1 answer
  • What is the first step in solving the inequality 2x + 3 2 17?
    8·1 answer
  • 25POINTS!!Which expression is equivalent to 3 x 5 x 5 x 5 x 5 X 5 X 5?
    7·2 answers
  • Help me please!!!! What percent of data is above the 38?
    8·2 answers
  • Solve this problem. <br><br> Don't answer if you don't know. NO IMPROPER ANSWERS.
    10·2 answers
  • 5. A total of 64 athletes enter a competition, and of the athletes
    12·1 answer
  • Any helppp pLeAsE? T^T
    7·1 answer
  • find the dimensions of a rectangle that has a length 3 inches longer than it’s width and has an area of 40in^2
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!