Question

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If $b>4$then$5b>20$

Short answer

The statement “If $b>4$then $5b>20$.” is true and the converse “If $5b>20$then $b>4$,” is true.

Step-by-step solution

Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement “If p, then q” will be “If q, then p”.

Step 2. State whether the statement is true or not.

Since $b>4$,let $b=5$,then

$\begin{array}{c}5b=5\left(5\right)\\ =25\end{array}$

Thus, $5b>20$.So, if $b=5$,then $5b>20$.Hence, the statement is true.

Step 3. Write the converse of the statement and verify.

The converse of the statement is: If $5b>20$then $b>4$,

Here,

$\begin{array}{c}5b>20\\ b>\frac{20}{5}\\ b>4\end{array}$

So, if $5b>20$then $b>4$. Thus, the converse statement is true.

Therefore, the statement: " If $b>4$,then $5b>20$." is true, but the converse of the statement: " If $5b>20$.then $b>4$," is true.