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A compound proposition is a statement formed by combining one or more simpler propositions using logical connectives. These connectives include AND, OR, and NOT. In our exercise, we combined three propositions: p, q, and 卢r, using the AND connective. The goal was to create a single proposition that is only true when specific conditions are met. For a compound proposition, it is essential to clearly understand the requirements and conditions that must be satisfied. In this case, the conditions were: p is true, q is true, and r is false. By understanding these conditions, we constructed individual clauses for each variable and then combined them using logical connectives to meet the desired outcome.

In propositional logic, each proposition can have a truth value: true (T) or false (F). The truth values help us evaluate the overall truth of a compound proposition based on its simpler components. In our specific problem, we determined the required truth values as follows:

• p = T (true)
• q = T (true)
• r = F (false)

Using these values, we examined how to construct a proposition that fits precisely these criteria. By identifying the truth values first, we were able to design the compound proposition accordingly. Here鈥檚 how the truth values guided our construction: By asserting that p should be true, we included the clause p. Since q should also be true, we added q. Lastly, because r must be false, we used the negation 卢r. These truth values set the foundation for our final compound proposition.

A conjunction is a logical connective that combines two or more propositions and returns true only if all the combined propositions are true. In mathematical notation, a conjunction is represented by the symbol 鈭�. In our solution, we used a conjunction to combine the clauses for p, q, and 卢r. This was done as follows:
To ensure the compound proposition is true only when all the individual conditions are met, we wrote: p 鈭� q 鈭� 卢r By using the conjunction, we formed a comprehensive statement that is true exclusively when p and q are true, and r is false. If any other combination of truth values is given, the conjunction will yield false. This precise control over truth outcomes is a powerful feature of logical connectives.