Fill in the blanks.
(i) The additive identity of the integers is `ul(P)`
(ii) The integer which is 8 less than - 24 is `ul(Q)`
(iii) Every integer less than zero is `ul(R)`

Options

A. `{:(P,Q,R),(0,-32,"negative"):}`
B. `{:(P,Q,R),(1,-32,"positive"):}`
C. `{:(P,Q,R),(0,-16,"negative"):}`
D. `{:(P,Q,R),(1,-32,"negative"):}`

Answer

Let's solve the question step by step.

### Step 1: Identify the additive identity of integers
The additive identity is the number that, when added to any integer, does not change the value of that integer. For any integer \( x \), if we add 0, we get \( x + 0 = x \). Thus, the additive identity of integers is:

**Answer for (i):** 0

### Step 2: Find the integer which is 8 less than -24
To find the integer that is 8 less than -24, we need to subtract 8 from -24. This can be expressed mathematically as:

\[ -24 - 8 = -32 \]

**Answer for (ii):** -32

### Step 3: Determine what every integer less than zero is
Every integer that is less than zero is known as a negative integer. This includes numbers like -1, -2, -3, and so on. Therefore, we can conclude that:

**Answer for (iii):** Negative

### Final Answers
(i) 0
(ii) -32
(iii) Negative

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