Let `P = { x : x in R , |x| < 2}`
`Q = {x:x in R , |x -1 |ge 2}`
`P uu Q = R - S` then set S is : (where R is the set of real number)

Options

A. `[-2,2]`
B. `[2,3]`
C. `[2,3)`
D. `(-1,2]`

Explanation

To solve the problem, we need to analyze the sets \( P \) and \( Q \) and find the set \( S \) such that \( P \cup Q = \mathbb{R} - S \).

### Step 1: Define the set \( P \)

The set \( P \) is defined as:
\[ P = \{ x : x \in \mathbb{R}, |x| < 2 \} \]
This means that \( P \) includes all real numbers \( x \) such that the absolute value of \( x \) is less than 2.

To express this in interval notation, we can rewrite it as:
\[ P = (-2, 2) \]