Question

Decide if the converse is true for the following true conditional statement: "if I am in my kitchen, then I am at home." If it is true, choose a valid biconditional statement.

1) The converse is false. A valid biconditional cannot be formed.
2) I am not at home if and only if I am not in my kitchen.
3) I am at home if and only if I am in my kitchen.
4) I am in my kitchen if and only if I am at home.

Answer 1

The converse of the statement "if I am in my kitchen, then I am at home" is false because being at home does not guarantee one is in the kitchen; therefore, a valid biconditional statement cannot be formed and the correct option is 1.

Step-by-step explanation:

The question is whether the converse of the true conditional statement "if I am in my kitchen, then I am at home" is also true, and if so, to choose a valid biconditional statement. The converse would say, "If I am at home, then I am in my kitchen." This converse is not necessarily true, as being at home does not guarantee that one is in the kitchen. Therefore, option 4, "I am in my kitchen if and only if I am at home," is not a valid biconditional statement because it incorrectly assumes that being in any location at home means one is specifically in the kitchen. However, one can still be at home without being in the kitchen, which makes the converse false. Thus, based on this information, we determine that answer option 1 is correct: The converse is false, and a valid biconditional cannot be formed.