In logic, compound propositions are formed by combining simpler propositions using logical connectives such as negation, conjunction, and disjunction. Each of these connectives plays a crucial role in shaping the truth values of compound propositions, which are fundamental in reasoning and mathematical proofs. Below, we will discuss each of these logical connectives in detail, along with sufficient examples.

Negation:
Negation is the logical operation that inverts the truth value of a given proposition. If a proposition \( P \) is true, its negation \( \neg P \) is false, and if \( P \) is false, \( \neg P \) becomes true. Negation is represented by the symbol \( \neg \) or sometimes a tilde \( \sim \).

For example:
- Let \( P \) be the proposition "It is raining." If \( P \) is true (i.e., it is raining), then \( \neg P \) ("It is not raining") will be false. 
- If \( P \) is false (i.e., it is not raining), then \( \neg P \) ("It is not raining") becomes true.

The truth table for negation is as follows:
\[
\begin{array}{|c|c|}
\hline
P & \neg P \\
\hline
T & F \\
F & T \\
\hline
\end{array}
\]
This table shows that if \( P \) is true, then \( \neg P \) is false, and if \( P \) is false, then \( \neg P \) is true.

Conjunction:
Conjunction is the logical operation that connects two propositions in a way that the compound proposition is true only if both of the individual propositions are true. Conjunction is