Question

a conditional statement is given below. give the inverse, contrapositive, and converse of the statement. also use the table above to 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 a toy block is not a square, then the toy block is not red. contrapositive: if a toy block is not red, then the toy block is not a square. converse: if a toy block is red, then the toy block is a square.

Explanation:

Step1: Recall definitions

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

Step2: Analyze truth - values

Just because a toy block is not a square (\(
eg p\)), it doesn't mean it's not red (\(
eg q\)), so the inverse \(
eg p
ightarrow
eg q\) is false. If a toy block is not red (\(
eg q\)), then it can't be a square according to the original statement, so the contrapositive \(
eg q
ightarrow
eg p\) is true. Just because a toy block is red (\(q\)), it doesn't mean it's a square, so the converse \(q
ightarrow p\) is false.

Answer:

Inverse: If a toy block is not a square, then the toy block is not red. False
Contrapositive: If a toy block is not red, then the toy block is not a square. True
Converse: If a toy block is red, then the toy block is a square. False