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3 years ago

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The empty set is the special set that contains no (i.e., zero) elements in the set. We use the notation empty set to represent t

he empty set. Let U be the universal set, and let A be a set of elements chosen from U. What is the value of empty set space x space A ?

1 answer:

Minchanka [31]3 years ago

5 0

Answer:

The value of a Cartesian product between an empty set and set A is equal to the empty set.

Step-by-step explanation:

The cartesian product is given by:

A×B= {(a,b): a∈A, b∈B}

This means that each element of set A is combined with an element of set B.

The empty set is the unique set having no elements and its size is zero.

Let Ф be the empty set and let A be a set of elements chosen from U.

A×Ф=Ф

Since the empty set has no elements, no ordered pairs can be formed and the result is the empty set.

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Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

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Now, find the margin of error M as such

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This is n when M = 0.1. So

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$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.1})^{2}$

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Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

This is n when M = 0.06. So

$M = z*\frac{\sigma}{\sqrt{n}}$

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$0.06\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.06}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.06})^{2}$

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Rounding up, 67

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$M = z*\frac{\sigma}{\sqrt{n}}$

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$0.05\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.05}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.05})^{2}$

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