Let's analyze each statement step by step to determine whether they are true or false.
### Step 1: Analyze the first statement
**Statement (i): The product of a positive integer and a negative integer is negative.**
- Let’s take a positive integer, for example, \( 3 \), and a negative integer, say \( -2 \).
- The product is \( 3 \times -2 = -6 \).
- Since the result is negative, this statement is **True**.
### Step 2: Analyze the second statement
**Statement (ii): The product of two negative integers is a negative integer.**
- Let’s take two negative integers, for example, \( -3 \) and \( -4 \).
- The product is \( -3 \times -4 = 12 \).
- Since the result is positive, this statement is **False**.
### Step 3: Analyze the third statement
**Statement (iii): The product of three negative integers is a negative integer.**
- Let’s take three negative integers, for example, \( -2 \), \( -3 \), and \( -4 \).
- The product is \( -2 \times -3 \times -4 \).
- First, calculate \( -2 \times -3 = 6 \) (which is positive).
- Now, \( 6 \times -4 = -24 \) (which is negative).
- Since the result is negative, this statement is **True**.
### Step 4: Analyze the fourth statement
**Statement (iv): Every integer when multiplied with -1 gives its multiplicative inverse.**
- Let’s take an integer, for example, \( 5 \).
- The product is \( 5 \times -1 = -5 \).
- The multiplicative inverse of \( 5 \) is \( \frac{1}{5} \), not \( -5 \).
- Therefore, this statement is **False**.
### Summary of Results
1. Statement (i): True
2. Statement (ii): False
3. Statement (iii): True
4. Statement (iv): False
