Q4B. - Algebra 1

Question

If a clothing store is selling wool coats, then it must be December.

Step-by-Step Solution

Answer

A counterexample to the given conditional statement can be if the clothing store is located in places like South Dakota.

Step 1. State the concept.

Not all places in the world have the same seasonal schedule. So, December is not the coldest month in all places in the world.

Step 2. List the given data.

The given statement is “If a clothing store is selling wool coats, then it must be December”. Here, the hypothesis is “a clothing store is selling wool coats” and the conclusion is “it must be December”.

Step 3. Simplify the given statement.

The given statement implies that December is the coldest month as wool clothes are worn in the winter when it is cold.

Step 4. Give a counterexample.

Consider a place like South Dakota. It experiences the heaviest snow and is thus coldest in the month of April, not December.

This implies that wool coats may be worn in months other than December. That would in turn imply that wool coats may be sold by shops in months other than December.

Even if in a place, December is the coldest month, winter products can be sold in the months leading up to winter or even after it as stock clearance.

So, the hypothesis, “a clothing store is selling wool coats” is true. However, the conclusion, “it must be December” is false.