Q2. - Algebra 1

Question

Monica claims: If you are in the drama club, then you are also on the academic team. Which student is a counterexample to this statement?

Step-by-Step Solution

Answer

Thomas is the counterexample for the given statement.

Step 1. Given information

The statement is “If you are in the drama club, then you are also on the academic team”.

The Venn diagram is:

Step 2. A counterexample for this statement.

From the given Venn diagram, there are four students Ronnie, Kim, Beth, and Thomas, which Kim and Beth are in both Drama and Academic, whereas Ronnie and Thomas are in Academics and Drama respectively. So, the statement is disproving but Thomas is in the drama club but not in the academic team.

Step 3. Conclusion.

Thomas is not in the Academic club, so is a counterexample for the statement.

Hence, option (J) is correct.