The student's question concerns the completion of a truth table for the converse of a conditional statement, which involves reversing the implication order and determining the new truth values for the given cases of p and q.
The student is asking about completing a truth table for the converse of a conditional statement. In a truth table for a conditional statement, the format is typically represented as 'if p then q' or symbolically as p → q. The converse of this statement is 'if q then p' or symbolically q → p.
To complete the truth table for the converse, we have to consider the truth values for q and p respectively since the order is reversed in the converse. Here are the correct truth values for the converse statement:
When q is true and p is true, the converse is true.
When q is true and p is false, the converse is false.
When q is false and p is true, the converse is true (since the antecedent is false, the entire conditional is true).
When q is false and p is false, the converse is true (for the same reason as above).