Which of the following is not a special characteristic of conditional statement?

Group of answer choices

If the antecedent is false, then p → q is automatically true.

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

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

If the consequent is true, then p → q is automatically true.

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.

Which of the following is not a special characteristic of conditional statement?

Group of answer choices:

1. If the antecedent is false, then p → q is automatically true.
2. p → q is true when the antecedent is true and the consequent is false.
3. p → q is false only when the antecedent is true and the consequent is false.
4. If the consequent is true, then p → q is automatically true.

Learn how conditional statements work in logic. This question explores the truth conditions of statements like p → q, including when such statements are true or false. It covers important logical concepts, suitable for students studying introductory logic at the college level.

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