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Select all the statements that are true.

A. -1 is less than [tex]-\frac{4}{5}[/tex].
B. -0.3 is less than [tex]\frac{1}{5}[/tex].
C. 0.6 is greater than 1.
D. 0 is greater than -0.5.
E. [tex]-\frac{3}{5}[/tex] is equal to -0.6.


Sagot :

Let's analyze each of the given statements to determine their truth values:

1. Statement 1: [tex]\(-1 < -\frac{4}{5}\)[/tex]

To check this, compare the two numbers:

- [tex]\(-1\)[/tex] is less than [tex]\(-0.8\)[/tex].
- Therefore, [tex]\(-1 < -\frac{4}{5}\)[/tex] is true.

2. Statement 2: [tex]\(-0.3 < \frac{1}{5}\)[/tex]

To check this, compare the two numbers:

- [tex]\(-0.3\)[/tex] is less than [tex]\(0.2\)[/tex].
- Therefore, [tex]\(-0.3 < \frac{1}{5}\)[/tex] is true.

3. Statement 3: [tex]\(0.6 > 1\)[/tex]

To check this, compare the two numbers:

- [tex]\(0.6\)[/tex] is less than [tex]\(1\)[/tex].
- Therefore, [tex]\(0.6 > 1\)[/tex] is false.

4. Statement 4: [tex]\(0 > -0.5\)[/tex]

To check this, compare the two numbers:

- [tex]\(0\)[/tex] is greater than [tex]\(-0.5\)[/tex].
- Therefore, [tex]\(0 > -0.5\)[/tex] is true.

5. Statement 5: [tex]\(-\frac{3}{5} == -0.6\)[/tex]

To check this, compare the two numbers:

- [tex]\(-\frac{3}{5}\)[/tex] is equal to [tex]\(-0.6\)[/tex].
- Therefore, [tex]\(-\frac{3}{5} == -0.6\)[/tex] is true.

Now, let's summarize the truth values of all statements:

1. True
2. True
3. False
4. True
5. True

The true statements are the 1st, 2nd, 4th, and 5th statements. Therefore, the indices of the true statements are:

[tex]\[ [0, 1, 3, 4] \][/tex]

Thus, the true statements are:
- [tex]\(-1 < -\frac{4}{5}\)[/tex]
- [tex]\(-0.3 < \frac{1}{5}\)[/tex]
- [tex]\(0 > -0.5\)[/tex]
- [tex]\(-\frac{3}{5} == -0.6\)[/tex]