Question

the table below gives the shape and color of toy blocks in a certain set. these are the only toy blocks in the set.

shape	color
square	red
circle	green
triangle	blue
clover	purple

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.

Explanation:

Step1: Recall definitions

Let \(p\): "A toy - block is a square" and \(q\): "The toy - block is red". The given statement is \(p
ightarrow q\).
The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\), which is "If a toy - block is not a square, then the toy - block is not red". This is false because a non - square block like a star or a circle can be green.
The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\), which is "If a toy - block is not red, then the toy - block is not a square". This is true since the only red block in the set is the square.
The converse of \(p
ightarrow q\) is \(q
ightarrow p\), which is "If a toy - block is red, then the toy - block is a square". This is true as the only red block in the set is the square.
For the given statement "If a toy block is a square, then the toy block is red", from the table, we can see that the only square block is red, so the given statement is True.

Answer:

Given statement: True
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", True