The following conditional statement is given: "If the fruit is an apple, then the fruit is red."

Question

Part A: Explain how to change a statement into the converse and write the converse of the given conditional statement. (5 points)

Part B: Is the converse of the conditional statement true or false? Explain your answer. If the converse is false, give a counterexample

Answer 1

Part A: To convert a conditional statement into the converse, you simply switch the hypothesis and conclusion of the statement.

Converse of the given conditional statement: "If the fruit is red, then the fruit is an apple."

Part B: The converse of the conditional statement is false. This is because just because a fruit is red, it does not necessarily mean that it is an apple. For example, a tomato is red but it is not an apple. This counterexample shows that the converse statement is false.