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
sasho [114]
3 years ago
8

Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A

2 and A 2 ⊆ A 3 . (b) the sets are pairwise disjoint. (c) There are two elements in common to each pair of sets and one element in all three sets.
Mathematics
1 answer:
lina2011 [118]3 years ago
8 0

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let n(A) the number of elements in A.

Remember, the number of elements in A_1 \cup A_2 \cup A_3 satisfies

n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)

Then,

a) If A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200, and if A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000

Since A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1

So

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600

b) Since the sets are pairwise disjoint

n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193

You might be interested in
Can someone help me with this
babunello [35]
たはたらさあらたはたはあらたさらやたはまさらたはまりあはらたはたさたはあらあらたはたひたはらたら、らま、らま、らまはたはたはさまらたらまはあはあらたはたひまひはたらたはまはたらまはた
6 0
2 years ago
James has decided to start saving for a cruise over the summer. His money is currently in the local bank modeled by the function
IgorLugansk [536]

Answer:

s ( x ) = 102,  a ( x ) = 8 ( x + 2 )

A function that combines the two:

f ( x ) = s ( x ) + a ( x ) = 102 + 8 ( x + 2 ) =

= 102 + 8 x + 16

final answer :       f ( x ) = 8 x + 118

7 0
3 years ago
From the beginning of the day the temperature rose 15° so that by 4 pm it was 87°. What was the temperature at the start of the
dezoksy [38]
The answer would be 72 degrees because it rose 15 from the begining

3 0
3 years ago
Please help me first person will get brainliest!!
olganol [36]

Answer:

6w-60x+6

Step-by-step explanation:

6(w-10x+1)

6w+6(-10)+6*1

6w-60x+6

8 0
3 years ago
Can anyone please help with this problem ASAP ?
lara31 [8.8K]

Answer:

4 would be $55.00 and 8 would be $75.00

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following best classifies a quadrilateral with coordinates A(2, 6), B(5, 1), C(10, 4), and D(7, 9)? Rectangle Paral
    5·1 answer
  • A standard fluorescent tube has a life length that is normally distributed with a mean of 7000 hours and a standard deviation of
    9·1 answer
  • James answered 14 items correctly on a 16-item quiz. what percent did he answer correctly?
    5·2 answers
  • Combine like terms and classify the polynomial by the number of terms. 4x^2 + 3 + 2x^2 - 7x + 1
    13·2 answers
  • The lab experiment is repeated again with the same two glass plates and the same sodium lamp but with a different human hair. Th
    12·1 answer
  • Valor de uma bicicleta em um periodo normal do ano é R$550,00 no black friday essa bicicleta recebeu 35% de desconto qual o valo
    6·1 answer
  • The time it takes glyceraldehyde-3-phosphate dehydrogenase to convert aldehyde to carbolic acid follows a normal distribution wi
    12·1 answer
  • Scroll down to see image
    5·1 answer
  • -9+(-14)=??<br><br> please help!
    12·1 answer
  • Use the expression 5(6 + 4x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: Ho
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!