Chapter 7: Problem 1

State whether each of the following statements is true or false. \(\begin{array}{lll}\text { (a) } 4>9 & \text { (b) } 4>4 & \text { (c) } 4 \geq 4\end{array}\) (d) \(0.001<10^{-5}\) (e) \(|-19|<100\) (f) \(|-19|>-20\) (g) \(0.001 \leq 10^{-3}\)

Short Answer

Expert verified

Question: Determine whether the following statements are true or false. a) 4 > 9 b) 4 > 4 c) 4 ≥ 4 d) 0.001 < 10^(-5) e) |-19| < 100 f) |-19| > -20 g) 0.001 ≤ 10^(-3) Answer: a) False b) False c) True d) False e) True f) True g) True

Step by step solution

Statement (a): 4 > 9

Compare the numbers 4 and 9. Since 4 is less than 9, the inequality 4 > 9 is false.

Statement (b): 4 > 4

Compare the number 4 to itself. Since 4 is equal to 4, the inequality 4 > 4 is false.

Statement (c): 4 ≥ 4

Compare the number 4 to itself. Since 4 is equal to 4, the inequality 4 ≥ 4 is true.

Statement (d): 0.001 < 10^(-5)

Convert 0.001 to scientific notation: \(1 \times 10^{-3}\). Compare this to \(10^{-5}\). Since -3 is greater than -5, the inequality 0.001 < 10^(-5) is false.

Statement (e): |-19| < 100

Evaluate the absolute value of -19, which is 19. Compare this to 100. Since 19 is less than 100, the inequality |-19| < 100 is true.

Statement (f): |-19| > -20

Evaluate the absolute value of -19, which is 19. Compare this to -20. Since 19 is greater than -20, the inequality |-19| > -20 is true.

Statement (g): 0.001 ≤ 10^(-3)

Convert 0.001 to scientific notation: \(1 \times 10^{-3}\). Compare this to \(10^{-3}\). Since both values are equal, the inequality 0.001 ≤ 10^(-3) is true.

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State whether each of the following statements is true or false. \(\begin{array}{lll}\text { (a) } 4>9 & \text { (b) } 4>4 & \text { (c) } 4 \geq 4\end{array}\) (d) \(0.001<10^{-5}\) (e) \(|-19|<100\) (f) \(|-19|>-20\) (g) \(0.001 \leq 10^{-3}\)

Short Answer

Step by step solution

Statement (a): 4 > 9

Statement (b): 4 > 4

Statement (c): 4 ≥ 4

Statement (d): 0.001 < 10^(-5)

Statement (e): |-19| < 100

Statement (f): |-19| > -20

Statement (g): 0.001 ≤ 10^(-3)

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