Question

a conditional statement is given below. give the converse, contrapositive, and inverse 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 triangle, then the toy block is blue.

Explanation:

Step1: Recall definitions

Let the original conditional statement be \(p
ightarrow q\), where \(p\) is "a toy - block is a triangle" and \(q\) is "the toy - block is blue".
The converse of \(p
ightarrow q\) is \(q
ightarrow p\), which is "If a toy - block is blue, then the toy - block is a triangle". This is false because there could be blue toy - blocks that are not triangles.
The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\), which is "If a toy - block is not a triangle, then the toy - block is not blue". This is false because there could be non - triangle toy - blocks that are blue.
The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\), which is "If a toy - block is not blue, then the toy - block is not a triangle". This is true because if a toy - block is not blue, according to the original statement's logic, it cannot be a triangle.

Answer:

Converse: False
Inverse: False
Contrapositive: True