A pair of dice is rolled once and the sum of the number which appear on the uppermost faces of the two dice is noted. Consider the following events
(i) `E_(1)` : Sum is odd
(ii) `E_(2)` : Sum is 5 or 6
(iii) `E_(3)` : Sum is greater than 11
(iv) `E_(4)` : Sum is less than 4
Find which of the given events are mutually exclusive.

Explanation

To determine which of the given events are mutually exclusive when a pair of dice is rolled, we need to analyze each event and see if they can occur simultaneously.

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When rolling two dice, the possible sums range from 2 (1+1) to 12 (6+6). The total number of outcomes when rolling two dice is \(6 \times 6 = 36\).

2. **Define the Events**:
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