The incorrect characteristic of a conditional statement from the options provided is:

"p → q is true when the antecedent is true and the consequent is false."

In a conditional statement $p \to q$ (if $p$, then $q$), the statement is false when the antecedent ( $p$ ) is true and the consequent ( $q$ ) is false.

Here’s a breakdown of the truth conditions for a conditional statement $p \to q$:

1. If $p$ (antecedent) is true and $q$ (consequent) is true, $p \to q$ is true.
2. If $p$ is true and $q$ is false, $p \to q$ is false.
3. If $p$ is false, $p \to q$ is true, regardless of $q$'s truth value.

Would you like more details or have any questions?

Follow-up questions:

1. What are the truth values of the different connectives in logic?
2. How do we create the truth table for a conditional statement?
3. Can a conditional statement be true if both the antecedent and consequent are false?
4. What is the difference between a biconditional and a conditional statement?
5. How do contrapositives affect the truth value of conditional statements?

Tip: In logic, conditionals can be tricky because if the antecedent is false, the statement is true regardless of the consequent.