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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.

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Step-by-step explanation:

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3 years ago
Which equation below would be best solved by using the addition property of equality?
Svetradugi [14.3K]

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Step-by-step explanation:

The addition property of equality means that if:

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A + C = B + C.

Then, the correct answer is the last option:

if

F - 23 = 45

Then we can add the same number to both sides, we can add 23 to both sides and in this way isolate F:

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8 0
3 years ago
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Of 136 randomly selected adults, 33 were found to have high blood pressure. Construct a 95% confidence interval for the true of
navik [9.2K]

Answer:

The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < \hat{p} < 0.314695

Step-by-step explanation:

The confidence interval for a proportion is given by the following formula;

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Where:

x = 33

n = 136

\hat{p} = x/n = 33/136 = 0.243

z value for 95% confidence is 1.96

Plugging in the values, we have;

CI=0.243\pm 1.96\times \sqrt{\frac{0.243(1-0.243)}{136}}

Which gives;

0.17059 < \hat{p} < 0.314695

Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < \hat{p} < 0.314695

From the above we have;

23.2 < x < 42.798

Since we are dealing with people, we round down as follows;

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4 0
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Answer:

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6 0
3 years ago
Which are equal to 3/2?
KIM [24]
Explanation:

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It is the same for the second option as well.

Third option :
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6/4 = 3/2

Fourth option:
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Answer:

Therefore, the third and fourth options are the correct choices.

Hope this helped!
6 0
3 years ago
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