Question

In Exercises 6 through 9, write the set in the form {x|P(x)}, where P(x) is a property that describes the elements of the set. 6. {2, 4, 6, 8, 10} 7.

Abstract algebra
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asked 2021-05-08

In Exercises 6 through 9, write the set in the form \(\{x|P(x)\}\), where P(x) is a property that describes the elements of the set.
6. \(\{2, 4, 6, 8, 10\}\)

7. \(\{a, e, i, o, u\}\)
8. \(\{1, 8, 27, 64, 125\}\)
9. \(\{-2, -1, 0, 1, 2\}\)

Answers (1)

2021-05-09

Exercise 6 \(\{2,4,6,8,10\}\)
We note that the set contain all even integers from 1 to 10, thus P(x) is then the property of an even integer from 1 to 10. \(\{x|x\) is an even integer and \(\displaystyle{1}\le{x}\le{10}\)}
Exercise 7 \(\{a,e,i,o,u,w\}\)
We note that the set contain all vowels, thus P(x) is then the property of a letter in the alphabet that is a vowel. \(\{x|x\) is a letter in the alphabet and x is a vowel}
Exercise 8 \(\{1,8,27,64,125\}\)
We note that the set contain cubes of the integers 1 to 5 \(\displaystyle{\left({1}^{{3}}={1},{2}^{{3}}={8},{3}^{{3}}={27},{4}^{{3}}={64}{\quad\text{and}\quad}{5}^{{3}}={125}\right)}\), thus P(x) is then the property that x is a cube of an integer from 1 to 5. \(\displaystyle{\left\lbrace{x}^{{3}}{\mid}{x}\right.}\) is an integer and \(\displaystyle{1}\le{x}\le{5}\rbrace\)
Exercise 9 \(\{-2,-1,0,1,2\}\)
We note that the set contain all integers from -2 to 2, thus P(x) is then the property of an integer from -2 to 2. \(\{x|x\) is an integer and \(\displaystyle-{2}\le{x}\le{2}\rbrace\)

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