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]
