Identify the quantifiers in the following statements.
(i) There exists a triangle which is not equilateral.
(ii) For all real numbers x and y , xy = yx.
(iii) There exists a real number which is not a rational number .
(iv) For every natural number which x,x + 1 is also a natural number.
(v) For all real number x with `x gt 3 , x^(2)` is greater than 9.
(vi) There exist a traingle which is not an isosceles traingle.
(vii) For all negative `x,x^(3)` is also a nagative integers.
(viii) There exists a statements in above statements which is not true.
(ix) There exists an even prime number other thab 2.
(x) There exists a real number x such that `x^(2) + 1=0`

Explanation

To identify the quantifiers in the given statements, we will analyze each statement one by one. There are two main types of quantifiers we will look for:

1. **Existential Quantifier**: "There exists" (∃)
2. **Universal Quantifier**: "For all" (∀)

Now, let's go through each statement step by step:

### Step-by-Step Solution:

1. **Statement (i)**: "There exists a triangle which is not equilateral."
- **Quantifier**: There exists (∃)

2. **Statement (ii)**: "For all real numbers x and y, xy = yx."
- **Quantifier**: For all (∀)

3. **Statement (iii)**: "There exists a real number which is not a rational number."
- **Quantifier**: There exists (∃)

4. **Statement (iv)**: "For every natural number x, x + 1 is also a natural number."
- **Quantifier**: For every (∀)

5. **Statement (v)**: "For all real numbers x with x > 3, x² is greater than 9."
- **Quantifier**: For all (∀)

6. **Statement (vi)**: "There exists a triangle which is not an isosceles triangle."
- **Quantifier**: There exists (∃)

7. **Statement (vii)**: "For all negative x, x³ is also a negative integer."
- **Quantifier**: For all (∀)

8. **Statement (viii)**: "There exists a statement in the above statements which is not true."
- **Quantifier**: There exists (∃)

9. **Statement (ix)**: "There exists an even prime number other than 2."
- **Quantifier**: There exists (∃)

10. **Statement (x)**: "There exists a real number x such that x² + 1 = 0."
- **Quantifier**: There exists (∃)

### Summary of Quantifiers:
- (i) There exists
- (ii) For all
- (iii) There exists
- (iv) For every
- (v) For all
- (vi) There exists
- (vii) For all
- (viii) There exists
- (ix) There exists
- (x) There exists