Question

The following conditional statement is given: "If it is Friday, then there is no school tomorrow."

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. (5 points)

Answer 1

To create the converse of a conditional statement, the antecedent and consequent are swapped. In this case, the converse statement, "If there is no school tomorrow, then it is Friday," is false because there could be other reasons for no school, such as holidays or emergencies.

Step-by-step explanation:

Part A: Forming the Converse of a Conditional Statement

To form the converse of a conditional statement, you swap the antecedent ("if" part) with the consequent ("then" part). For the given statement, "If it is Friday, then there is no school tomorrow", the converse would be "If there is no school tomorrow, then it is Friday".

Part B: Truth Value of the Converse

The converse of a conditional statement is not necessarily true, and in this case, it is false. This is because there can be other reasons for no school tomorrow, such as holidays or emergency closures. A counterexample might be, "If it is a snow day, then there is no school tomorrow," which can occur on any day of the week.