Question

Write a counterexample for the converse of the conditional statement you chose for the Venn Diagram in the previous question.

Answer 1

To provide you with a counterexample for the converse of a conditional statement, let’s first define a conditional statement.

For example, consider the conditional statement:

**Original Statement (P → Q):** If it is raining (P), then the ground is wet (Q).

The converse of this statement is:

**Converse (Q → P):** If the ground is wet (Q), then it is raining (P).

**Counterexample for the Converse:** The ground can be wet for a variety of reasons beyond rain, such as someone watering the lawn or a sprinkler system being activated. Therefore, if the ground is wet, it does not necessarily mean that it is raining.

In summary, the original statement is true (rain leads to a wet ground), but the converse is not true, as a wet ground can result from other causes. Thus, “the ground is wet” does not imply “it is raining.” This serves as a counterexample to the converse of the original statement.