The value of `1 + [1 + 1 + { 1 + (1 + 1 + 2 ) } ]`is-

Options

A. 8
B. `8/5`
C. `1`
D. None of these

Answer

To solve the expression \( 1 + [1 + 1 + \{ 1 + (1 + 1 + 2) \}] \), we will follow the order of operations, which is parentheses, brackets, and then addition.

### Step-by-Step Solution:

1. **Start with the innermost parentheses**:
\[ (1 + 1 + 2) \]
Calculate this first:
\[ 1 + 1 + 2 = 4 \]

2. **Substitute the result back into the expression**:
Now, replace \( (1 + 1 + 2) \) with \( 4 \):
\[ 1 + [1 + 1 + \{ 1 + 4 \}] \]

3. **Calculate the expression inside the curly braces**:
\[ 1 + 4 = 5 \]
Now, substitute this back:
\[ 1 + [1 + 1 + 5] \]

4. **Now, simplify the expression inside the brackets**:
\[ 1 + 1 + 5 = 7 \]
Substitute this back:
\[ 1 + 7 \]

5. **Finally, add the last two numbers**:
\[ 1 + 7 = 8 \]

### Final Answer:
The value of the expression \( 1 + [1 + 1 + \{ 1 + (1 + 1 + 2) \}] \) is \( 8 \).

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