Question

Find a counterexample for each conditional statement.

If a number y is multiplied by $\frac{\mathbf{1}}{\mathbf{3}}\mathbf{,}$then $\frac{\mathbf{1}}{\mathbf{3}}\mathit{y}\mathbf{<}\mathit{y}$.

Short answer

A counterexample is “If a number is multiplied by $\frac{1}{3}$, then $\frac{1}{3}y>y$, where $y<0$”.

Step-by-step solution

Step 1. Given.

If a number $y$is multiplied by $\frac{1}{3}$, then $\frac{1}{3}y<y$.

Step 2. To find.

We have to find a counter-example for the condition “If a number $y$is multiplied by $\frac{1}{3}$, then $\frac{1}{3}y<y$.”

Step 3. Calculation.

The given statement is “If a number $y$is multiplied by $\frac{1}{3}$, then $\frac{1}{3}y<y$”.

To get a counterexample we will define other conclusions than $\frac{1}{3}y<y$. We can define one counterexample that: “if a number is multiplied by $\frac{1}{3}$, then $\frac{1}{3}y>y$, where $y<0$”.

That means $\frac{1}{3}y>y$ is not necessarily true.