Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
determine which statements are the converse, inverse, and contrapositive of the following statement.
if it is after midnight, anissa is sleeping.
if anissa is sleeping, it is after midnight.
if anissa is not sleeping, it is not after midnight.
if it is not after midnight, anissa is sleeping.
if it is not after midnight, anissa is not sleeping.
if anissa is sleeping, it is not after midnight.
contrapositive
converse
inverse

Explanation:

1. Let the original statement be \( p \to q \), where \( p \): "It is after midnight", \( q \): "Anissa is sleeping".

• Converse: Swaps \( p \) and \( q \), so \( q \to p \). The statement "If Anissa is sleeping, it is after midnight" matches \( q \to p \).
• Inverse: Negates both \( p \) and \( q \), so \(

eg p \to
eg q \). The statement "If it is not after midnight, Anissa is not sleeping" matches \(
eg p \to
eg q \).

• Contrapositive: Negates and swaps \( p \) and \( q \), so \(

eg q \to
eg p \). The statement "If Anissa is not sleeping, it is not after midnight" matches \(
eg q \to
eg p \).

Answer:

• Contrapositive: If Anissa is not sleeping, it is not after midnight.
• Converse: If Anissa is sleeping, it is after midnight.
• Inverse: If it is not after midnight, Anissa is not sleeping.