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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.

Short Answer

Expert verified

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

Step by step solution

01

Step 1. State the concept.

Not all writing projects are more than two pages long.

02

Step 2. List the given data.

The given statement is 鈥淚f a teacher assigns a writing project, then it must be more than two pages long鈥. Here, the hypothesis is 鈥渁 teacher assigns a writing project鈥 and the conclusion is 鈥渋t must be more than two pages long鈥.

03

Step 3. Simplify the given statement.

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

04

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, 鈥渁 teacher assigns a writing project鈥 is true. However, the conclusion, 鈥渋t must be more than two pages long鈥 is false.

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