How many possible output will be produced in a proposition of three statements?

To determine the number of possible outputs produced from a proposition involving three statements, we can follow these steps:

1. ### Break Down the Problem

We need to analyze the number of possible combinations of truth values for three independent statements. Each statement can either be true (T) or false (F).

2. ### Relevant Concepts

For each statement:

• True (T) = 1
• False (F) = 0

With n statements, each having two possibilities (T or F), the total number of combinations can be calculated using the formula: $\text{Total combinations} = 2^n$

3. ### Analysis and Detail

Here, we have:

• $n = 3$

Substituting into the formula gives: $\text{Total combinations} = 2^3 = 8$

4. ### Verify and Summarize

Let's verify by enumerating the possible combinations of three statements (A, B, C):

1. T, T, T
2. T, T, F
3. T, F, T
4. T, F, F
5. F, T, T
6. F, T, F
7. F, F, T
8. F, F, F

This confirms that there are indeed 8 possible outputs.

Final Answer

The total number of possible outputs from a proposition involving three statements is $8$.