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# 01. Let π = {β2; 1; 0;1/2;3/4; 2;10/3; 4; β5}. Explain the elements of each of the following sets: a) {π₯ β π/π₯ β 4 < 0} b) {π₯ β π/π₯ 2 β 6π₯ + 8 < 0} c) {π₯ β π/4 β π₯ β€ 0} d) {π₯ β π/π₯ 2 + 1 β€ 0}

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## Answer to a math question 01. Let π = {β2; 1; 0;1/2;3/4; 2;10/3; 4; β5}. Explain the elements of each of the following sets: a) {π₯ β π/π₯ β 4 < 0} b) {π₯ β π/π₯ 2 β 6π₯ + 8 < 0} c) {π₯ β π/4 β π₯ β€ 0} d) {π₯ β π/π₯ 2 + 1 β€ 0}

Eliseo
4.6
68 Answers
Given set π = {β2; 1; 0; 1/2; 3/4; 2; 10/3; 4; β5}

a) {π₯ β π/π₯ - 4 < 0}
To solve this, first, we need to find the elements in π where π₯ - 4 < 0.
π₯ - 4 < 0
π₯ < 4

The elements in set π that satisfy π₯ < 4 are {-2; 1; 0; 1/2; 3/4; 2, 10/3}.

b) {π₯ β π/π₯^2 - 6π₯ + 8 < 0}
To solve this, first, we need to find the elements in π where π₯^2 - 6π₯ + 8 < 0.
$π₯ - 4$$π₯ - 2$ < 0
The solutions to this inequality are π₯ β $2, 4$.
Thus, the elements in set π that satisfy this inequality are {3/4}.

c) {π₯ β π/4 - π₯ β€ 0}
To solve this, first, we need to find the elements in π where 4 - π₯ β€ 0.
4 - π₯ β€ 0
π₯ β₯ 4
The only element in set π that satisfies this inequality is {4}.

d) {π₯ β π/π₯^2 + 1 β€ 0}
To solve this, first, we need to find the elements in π where π₯^2 + 1 β€ 0.
This inequality has no real solutions because π₯^2 + 1 is always greater than 0 for all real values of π₯.
Therefore, there are no elements in π that satisfy this inequality.

\textbf{Answer:}
a) {-2; 1; 0; 1/2; 3/4; 2; 10/3}
b) {3/4}
c) {4}
d) No elements in set π satisfy the inequality.

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