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
s344n2d4d5 [400]
3 years ago
6

a. Determine all bijections from the {1,2,3} into {a,b,c}. b. Determine all bijections from {1, 2, 3} into {a,b,c,d}.

Mathematics
1 answer:
avanturin [10]3 years ago
3 0

Part A

There are 6 bijections from {1,2,3} to {a,b,c}. This is effectively the same as asking the question "how many ways are there to arrange {a,b,c} where order matters?" We use a factorial to answer this question.

3 factorial = 3! = 3*2*1 = 6

You can also use a permutation, which is composed of factorials, to get the same answer.

======================================================

Part B

There are no bijections from {1,2,3} to {a,b,c,d}. Why is this? Because a bijection has two properties: it must be one-to-one, and it must be onto. The term "onto" in mathematics means "every value in the range is targeted". In the case of the range {a,b,c,d} it is not possible for each value to show up. This is because there are only three items in the domain {1,2,3}. You'll always be one letter short.

As you can probably guess, a bijection is only possible if and only if n(D) = n(R), where D and R are the domain and range respectively. The notation n(D) represents the count or number of items in set D.

You might be interested in
Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gu
Murljashka [212]

Answer:

The value of g_s is g_s=\frac{30}{21} \:\frac{m}{s^2}.

Step-by-step explanation:

We know that the position function is given by

s(t)=30t-\frac{g_s}{2} t^2

Velocity is defined as the rate of change of position. Therefore,

v(t)=\frac{d}{dt}(s(t))

So, the velocity function is

v(t)=\frac{d}{dt}(s(t))\\\\v(t)=\frac{d}{dt}(30t-\frac{g_s}{2} t^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(30t\right)-\frac{d}{dt}\left(\frac{g_s}{2}t^2\right)\\\\v(t)=30-g_st

When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,

v(t)=30-g_st=0\\\\g_s=\frac{30}{t}

We know that the ball bearing reaches its maximum height 21 seconds after being launched (t = 21 s).

So, the value of g_s is g_s=\frac{30}{21} \:\frac{m}{s^2}.

5 0
3 years ago
A football player weighed 170 pounds in May. During the summer, he gained 25 5/12 pounds. During the first week of fall practice
alisha [4.7K]

Answer:

he now weighs a total of 182 pounds.

hopefully thats right if not im sorry :c

8 0
3 years ago
3. Kevin weighs 57 kilograms (kg) and his father weighs 85 kg. How much less
Lelu [443]

Answer:

his father weighs 28 kg more :)

4 0
2 years ago
X-4y =-6 ( ,2) (-2, )
marin [14]

Answer:5x-20y=12

Step-by-step explanation:

5 0
3 years ago
Use the formula d = rt to find the distance d a long-distance runner can run at a rate r of 9 1/2 miles per hour for time t of 1
boyakko [2]

multiply the 2 numbers

9 1/2 * 1 3/4 =

19/2 * 7/4 = 133/8 = 16 5/8 miles

6 0
3 years ago
Other questions:
  • PLEASE ANSWER. QUESTION ABOUT GRAPHS.
    8·1 answer
  • Help please! Will give brainly!!! Which of the following equations have the same solution? Give reasons for your answer that do
    10·1 answer
  • How do I solve 8/3=(y-9)/(7y+4)
    6·1 answer
  • Four times a number, n, added to 3 is 47
    6·1 answer
  • How do you write 10×6 tens in unit and standard form
    11·2 answers
  • CFISD
    5·1 answer
  • Find the value of x and y
    7·1 answer
  • The distance from c to d?
    15·1 answer
  • A right prism is shown below
    8·1 answer
  • What is the angle Between two parallel lines? Hmm?ಠ_ಠ
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!