• Given the Conditional Statement: "If an item is a bracelet, then the item is made from gold", you need to remember that a Conditional Statement has two parts:
- A hypothesis.
- A conclusion.
In this case, you can identify that:
- The hypothesis is: "An item is a bracelet".
- The conclusion is: "The item is made from gold".
You can identify in the table that a bracelet is made from gold. Therefore, the statement is true.
Then:
• In order to give the Converse of the Conditional Statement, you need to change the order of the hypothesis and the conclusion. The conclusion must be located before the hypothesis.
Therefore, it is: If an item is made from gold, then the item is a bracelet.
You can observe on the table that a bracelet and a necklace are made from gold. Hence, the statement is false.
• In order to give the Inverse of the Conditional Statement, the hypothesis and the conclusion must be in negation form: ,If an item is not a bracelet, then the item is not made from gold.
You can see on the table that a necklace is made from gold too. Then, the statement is false.
• In order to give the Contrapositive of the Conditional Statement, you must change the order of the places of the conclusion and the hypothesis of the Inverse Statement found above: ,If an, ,item is, ,not made from gold, then the item is not a bracelet.
You can identify in the table that a bracelet is made from gold. Therefore, the statement is true.
Hence, the answers are:
• The given statement is True.
• Converse: ,If an item is made from gold, then the item is a bracelet. ,(False)
• Inverse: ,If an item is not a bracelet, then the item is not made from gold. ,(False)
• Contrapositive: ,If an, ,item is, ,not made from gold, then the item is not a bracelet. ,(True)