Q11. - Algebra 1

Question

Example 4 Find a counterexample for each conditional statement.

If a teacher assigns a writing project, then it must be more than two pages long.

Step-by-Step Solution

Answer

A counterexample to the given conditional statement can be when the project assigned is one page long.

Step 1. State the concept.

Not all writing projects are more than two pages long.

Step 2. List the given data.

The given statement is “If a teacher assigns a writing project, then it must be more than two pages long”. Here, the hypothesis is “a teacher assigns a writing project” and the conclusion is “it must be more than two pages long”.

Step 3. Simplify the given statement.

The given statement implies that all writing projects are more than two pages long.

Step 4. Give a counterexample.

A writing project assigned by a teacher can be of any length. Sometimes it may be more than two pages long and sometimes it may be a short project less than two pages long.

Suppose a teacher assigns a one-page long writing project. Thus, it is not true that whenever a teacher assigns a writing project, it is more than two pages long.

So, the hypothesis, “a teacher assigns a writing project” is true. However, the conclusion, “it must be more than two pages long” is false.