The image contains a multiple-choice question asking about which types of statements are either both true or both false. The options listed include various logical relationships between conditional statements, their converses, inverses, and contrapositives.

Understanding the Concepts:

1. Conditional Statement (P → Q): This is a statement of the form "If P, then Q."
2. Converse (Q → P): This flips the conditional statement, stating "If Q, then P."
3. Inverse (¬P → ¬Q): This negates both the hypothesis and conclusion of the conditional statement, saying "If not P, then not Q."
4. Contrapositive (¬Q → ¬P): This flips and negates both the hypothesis and conclusion, stating "If not Q, then not P."

Key Relationships:

• A conditional statement is logically equivalent to its contrapositive.
• A converse is logically equivalent to the inverse.

Answer:

The types of statements that are either both true or both false are:

• The conditional statement and the contrapositive of the conditional statement.
• The converse of a conditional statement and the inverse of the conditional statement.

Thus, the correct choices are:

• The conditional statement and the contrapositive of the conditional statement.
• The converse of a conditional statement and the inverse of the conditional statement.

Would you like further details or explanations on any specific part?

Here are 5 related questions to expand on this topic:

1. What are some examples of conditional statements and their contrapositives in real-life situations?
2. How do truth tables help verify the logical equivalence of these statements?
3. What is the difference between logical equivalence and material implication?
4. Can a converse of a conditional statement ever be logically equivalent to the conditional statement itself?
5. How does understanding these relationships help in mathematical proofs?

Tip: When working with logical statements, creating a truth table is a useful way to determine the relationships between different forms of statements.