Question

circle\tred
star\tpurple
clover\tred
square\tgreen
triangle\tblue

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\tif a toy block is a clover, then the toy block is red.\t○ true\t○ false
converse\tif select then select\t○ true\t○ false
contrapositive\tif select then select\t○ true\t○ false
inverse\tif select then select\t○ true\t○ false

Explanation:

Given Statement Analysis:

The given statement is "If a toy block is a clover, then the toy block is red." From the table, the clover is red, so this statement is True.

Converse:

The converse of a conditional statement \( p \to q \) is \( q \to p \). Here, \( p \): "a toy block is a clover", \( q \): "the toy block is red". So the converse is "If a toy block is red, then the toy block is a clover."
From the table, red toy blocks are circle and clover (not just clover), so this is False.

Contrapositive:

The contrapositive of \( p \to q \) is \(
eg q \to
eg p \). So it is "If a toy block is not red, then the toy block is not a clover."
Non - red toy blocks are star (purple), square (green), triangle (blue). None of these are clover, so this statement is True (since the contrapositive of a true statement is true, and we can also verify from the table).

Inverse:

The inverse of \( p \to q \) is \(
eg p \to
eg q \). So it is "If a toy block is not a clover, then the toy block is not red."
From the table, the circle is not a clover but is red. So this statement is False.

Filling the Table:

• Given statement: If a toy block is a clover, then the toy block is red. → Select "True".
• Converse: If a toy block is red, then the toy block is a clover. → Select "False".
• Contrapositive: If a toy block is not red, then the toy block is not a clover. → Select "True".
• Inverse: If a toy block is not a clover, then the toy block is not red. → Select "False".

Final Answers for Each Part:

• Given statement: True
• Converse: If a toy block is red, then the toy block is a clover; False
• Contrapositive: If a toy block is not red, then the toy block is not a clover; True
• Inverse: If a toy block is not a clover, then the toy block is not red; False

Answer:

Given Statement Analysis:

The given statement is "If a toy block is a clover, then the toy block is red." From the table, the clover is red, so this statement is True.

Converse:

The converse of a conditional statement \( p \to q \) is \( q \to p \). Here, \( p \): "a toy block is a clover", \( q \): "the toy block is red". So the converse is "If a toy block is red, then the toy block is a clover."
From the table, red toy blocks are circle and clover (not just clover), so this is False.

Contrapositive:

The contrapositive of \( p \to q \) is \(
eg q \to
eg p \). So it is "If a toy block is not red, then the toy block is not a clover."
Non - red toy blocks are star (purple), square (green), triangle (blue). None of these are clover, so this statement is True (since the contrapositive of a true statement is true, and we can also verify from the table).

Inverse:

The inverse of \( p \to q \) is \(
eg p \to
eg q \). So it is "If a toy block is not a clover, then the toy block is not red."
From the table, the circle is not a clover but is red. So this statement is False.

Filling the Table:

• Given statement: If a toy block is a clover, then the toy block is red. → Select "True".
• Converse: If a toy block is red, then the toy block is a clover. → Select "False".
• Contrapositive: If a toy block is not red, then the toy block is not a clover. → Select "True".
• Inverse: If a toy block is not a clover, then the toy block is not red. → Select "False".

Final Answers for Each Part:

• Given statement: True
• Converse: If a toy block is red, then the toy block is a clover; False
• Contrapositive: If a toy block is not red, then the toy block is not a clover; True
• Inverse: If a toy block is not a clover, then the toy block is not red; False