Question

The table below gives the material of each item in Nicole's jewelry box.

These are the only items in Nicole's jewelry box.
A conditional statement is given below. Give the converse, inverse, and contrapositive of the statement. Also use the table above to decide if each statement is true or false.
Assume that any item mentioned comes from Nicole's jewelry box.
See image! The statement 'If an item is a pendant, then the item is made from copper. is true.

Answer 1

Converse : If an item is made from copper ,then the item is a pendent. False

• We are not certain about the item made from copper to be a pendent but it's true the other way.
• In a Converse statement,we switch the order of the hypothesis or claim i.e. here ,we switched the order by putting the latter part first and the former one at the end.

Inverse : If an item is not a pendent, then the item is not made from copper. False

• Again,we aren't provided with sufficient information to support the statement that articles which are non pendent are not copper made .
• In an inverse statement, we turn the statement into a negative one .

Contrapositive : If an item is not made from copper,then the item is not a pendent. True

• In this case, the statement becomes true as the statement claims that the pendent has to be copper made in order to be and thus, if an item isn't made from copper then it can't be a pendent.
• In a contrapositive statement,we alter the order of the statement and turn it negative.

Answer 2

• Converse: If an item is made from copper, then the item is a pendant. (False)
• Inverse: If an item is not a pendant, then the item is not made from copper. (False)
• Contrapositive: If the item is not made from copper, then it is not a pendant. (True)

Explanation:

Given conditional statement:

• If an item is a pendant, then the item is made from copper.

The hypothesis of a conditional statement appears after the "if" part, and the conclusion of a conditional statement appears after the "then" part. Therefore:

• Hypothesis: An item is a pendant.
• Conclusion: The item is made from copper.

Converse

The converse of a conditional statement is a new statement formed by reversing the order of the original hypothesis and conclusion. Therefore, the converse is:

• If an item is made from copper, then the item is a pendant.

The converse is false since copper is a material that can be used for various objects, not just pendants. Just because an item is made from copper, it doesn't mean it is a pendant.

Inverse

The inverse of a conditional statement is a new statement formed by negating both the hypothesis and the conclusion of the original statement. Therefore, the inverse is:

• If an item is not a pendant, then the item is not made from copper.

The inverse is false because the fact that an item is not a pendant doesn't necessarily mean it is not made from copper.

Contrapositive

The contrapositive of a conditional statement is a new statement formed by both negating and reversing the order of the original hypothesis and conclusion. In other words, we switch the hypothesis and conclusion of the inverse statement. Therefore, the contrapositive is:

• If the item is not made from copper, then it is not a pendant.

This contrapositive is true. According to the original statement, for the object to be a pendant, it has to be made of copper. So, if it is not made of copper, it can't be a pendant.