The following conditional statement is given: "If the vehicle is a school bus, then the vehicle must be yellow."

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. (5 points)

Answer 1

Part A: Converse of the Conditional Statement

To change a conditional statement into its converse, you swap the hypothesis and the conclusion. The general form of a conditional statement is "If P, then Q," where P is the hypothesis and Q is the conclusion. The converse of this statement is "If Q, then P."

Given the original statement: "If the vehicle is a school bus (P), then the vehicle must be yellow (Q)."

The converse would be: "If the vehicle is yellow (Q), then the vehicle is a school bus (P)."

Part B: Truth Value of the Converse

The converse "If the vehicle is yellow, then the vehicle is a school bus" is false.

Explanation: The premise that a vehicle is yellow does not guarantee that it is a school bus. Many types of vehicles can be yellow, including taxis, certain models of cars, and construction vehicles.

Counterexample: A yellow taxi is a vehicle that is yellow but is not a school bus. This serves as a counterexample to demonstrate that the converse statement does not hold true, as it shows a situation where the hypothesis is true (the vehicle is yellow) while the conclusion is false (the vehicle is not a school bus).