One activity or project for propositional connectives in logic math could be creating truth tables for different logical expressions.

Here’s how you can do it:

1. Start by choosing a logical expression that involves propositional connectives, such as “p ∧ q → r”, where p, q, and r are propositional variables.

2. Create a truth table with columns for p, q, r, and the logical expression. Fill in the rows with all possible combinations of truth values for p and q.

3. Determine the truth value of the logical expression for each row by applying the propositional connectives. For example, if p is true, q is false, and r is true, then “p ∧ q → r” would be true.

4. Repeat steps 2 and 3 for different logical expressions involving different propositional connectives, such as “p ∨ q”, “¬p”, or “p ↔ q”.

5. Analyze the truth tables to identify patterns and relationships between the truth values of the propositional variables and the logical expressions.

6. Discuss the results and conclusions drawn from the truth tables, such as the conditions under which the logical expressions are true or false.

This activity allows students to practice applying propositional connectives and understand how they affect the truth values of logical expressions. It also helps develop critical thinking and problem-solving skills in the context of logic math.