Question

write the negation of each part of the conditional. then write the converse, the inverse, and the contrapositive. determine the truth value of each new statement.

1. if a figure is a square, then it is a rectangle.
2. if the game is field hockey then the game is a team sport.

Explanation:

Step1: Identify the hypothesis and conclusion

The conditional statement is “If a figure is a square, then it is a rectangle.”
Let \(p\): A figure is a square.
Let \(q\): A figure is a rectangle.

Step2: Find the negation of \(p\) and \(q\)

\(
eg p\): A figure is not a square.
\(
eg q\): A figure is not a rectangle.

Step3: Write the converse

The converse of \(p
ightarrow q\) is \(q
ightarrow p\).
Converse: “If a figure is a rectangle, then it is a square.”
This is false (e.g., a non - square rectangle).

Step4: Write the inverse

The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\).
Inverse: “If a figure is not a square, then it is not a rectangle.”
This is false (e.g., a non - square rectangle).

Step5: Write the contrapositive

The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\).
Contrapositive: “If a figure is not a rectangle, then it is not a square.”
This is true.

Answer:

• Converse: “If a figure is a rectangle, then it is a square.” (False)
• Inverse: “If a figure is not a square, then it is not a rectangle.” (False)
• Contrapositive: “If a figure is not a rectangle, then it is not a square.” (True)