Q10. - Algebra 1

Question

Find a counterexample for each conditional statement.

If Jack is at the park, then he is flying a kite.

Step-by-Step Solution

Answer

A counterexample to the given conditional statement can be when Jack is running as a form of physical exercise, at the park.

Step 1. State the concept.

One does not go to the park just to fly kites.

Step 2. List the given data.

The given statement is “If Jack is at the park, then he is flying a kite”. Here, the hypothesis is “Jack is at the park” and the conclusion is “he is flying a kite”.

Step 3. Simplify the given statement.

The given statement implies that Jack only goes to the park to fly a kite.

Step 4. Give a counterexample.

A park is a place where there are many things to do. One can enjoy the rides if there are any, one can play sports like cricket or soccer with their friends. One can even go to the park for a run or exercise.

So, Jack can go to the park to do any of these. Suppose that Jack goes to the park to run as a form of physical exercise. So, it is not true that whenever he is at the park, he must be flying a kite.

So, the hypothesis, “Jack is at the park” is true. However, the conclusion, “he is flying a kite” is false.