Given Universal set `={-6, -5""3/4, -sqrt(4), (-3)/5, (-3)/8, 0, 4/5, 1, 1""2/5, sqrt(8), 3.01, pi, 8.47}`.
From the given set, find :
(i) Set of rational numbers
(ii) Set of irrational numbers
(iii) Set of integers
(iv) Set of non-negative integers.

Answer

To solve the problem, we will analyze the given universal set and categorize the numbers into rational numbers, irrational numbers, integers, and non-negative integers.

### Given Universal Set:
\[ U = \{-6, -\frac{23}{4}, -\sqrt{4}, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, \frac{12}{5}, \sqrt{8}, 3.01, \pi, 8.47\} \]

### Step 1: Identify Rational Numbers
Rational numbers are numbers that can be expressed as the quotient of two integers (i.e., in the form \(\frac{p}{q}\), where \(q \neq 0\)).

- From the universal set, we identify:
- \(-6\) (integer)
- \(-\frac{23}{4}\) (fraction)
- \(-\sqrt{4} = -2\) (integer)
- \(-\frac{3}{5}\) (fraction)
- \(-\frac{3}{8}\) (fraction)
- \(0\) (integer)
- \(\frac{4}{5}\) (fraction)
- \(1\) (integer)
- \(\frac{12}{5}\) (fraction)
- \(3.01\) (can be expressed as \(\frac{301}{100}\))
- \(8.47\) (can be expressed as \(\frac{847}{100}\))

**Set of Rational Numbers:**
\[ R = \{-6, -\frac{23}{4}, -2, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, \frac{12}{5}, 3.01, 8.47\} \]

### Step 2: Identify Irrational Numbers
Irrational numbers cannot be expressed as a fraction of two integers.

- From the universal set, we identify:
- \(\sqrt{8} = 2\sqrt{2}\) (not a perfect square, thus irrational)
- \(\pi\) (known to be irrational)

**Set of Irrational Numbers:**
\[ I = \{2\sqrt{2}, \pi\} \]

### Step 3: Identify Integers
Integers are whole numbers that can be positive, negative, or zero.

- From the universal set, we identify:
- \(-6\) (negative integer)
- \(-2\) (from \(-\sqrt{4}\))
- \(0\) (zero)
- \(1\) (positive integer)

**Set of Integers:**
\[ Z = \{-6, -2, 0, 1\} \]

### Step 4: Identify Non-Negative Integers
Non-negative integers are integers that are either positive or zero.

- From the integers identified, we have:
- \(0\) (zero)
- \(1\) (positive integer)

**Set of Non-Negative Integers:**
\[ N = \{0, 1\} \]

### Final Results
1. **Set of Rational Numbers:**
\[ R = \{-6, -\frac{23}{4}, -2, -\frac{3}{5}, -\frac{3}{8}, 0, \frac{4}{5}, 1, \frac{12}{5}, 3.01, 8.47\} \]

2. **Set of Irrational Numbers:**
\[ I = \{2\sqrt{2}, \pi\} \]

3. **Set of Integers:**
\[ Z = \{-6, -2, 0, 1\} \]

4. **Set of Non-Negative Integers:**
\[ N = \{0, 1\} \]