Question

a conditional statement is given below. give the inverse, contrapositive, and converse of the statement. also use the table above to decide if each statement is true or false. assume that any toy block mentioned comes from the set. given statement: if a toy block is a square, then the toy block is red. inverse: if select then select contrapositive: if select then select converse: if select then select true false true false true false true false

Explanation:

Step1: Recall definitions

Let the original conditional statement be \(p
ightarrow q\) where \(p = \) "a toy - block is a square" and \(q=\) "the toy - block is red".
The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\), the converse is \(q
ightarrow p\), and the contrapositive is \(
eg q
ightarrow
eg p\).

Step2: Find the inverse

The inverse of "If a toy - block is a square, then the toy - block is red" is "If a toy - block is not a square, then the toy - block is not red". Just because a toy - block is not a square doesn't mean it can't be red, so the inverse is False.

Step3: Find the converse

The converse is "If a toy - block is red, then the toy - block is a square". There can be red toy - blocks that are not squares, so the converse is False.

Step4: Find the contrapositive

The contrapositive is "If a toy - block is not red, then the toy - block is not a square". If a toy - block is not red, it can't be a red square, so the contrapositive is True.

Answer:

Inverse: False
Converse: False
Contrapositive: True