Chapter 2.1, Problem 26WE

To determine

To state: The converse of statement and state whether it is true or false

Answer to Problem 26WE

The statement is false.

The converse of the given statement is true

Explanation of Solution

Given information:

The given statement is:

  $″ab=0,$ implies that $a=0$ or $b=0″$

  $″ab=0,$ implies that $a=0$ or $b=0″$

Here $ab=0$

Then either $a=0$ or $b=0$ both are 0

That is both $a$ and $b$ may be 0

Therefore, the statement is false.

Now here $p$ is $″ab=0″$ and $q$ is $″a=0″$ or $″b=0″$

The converse is of the form "if $q$ ,then $p″$

Therefore, the converse of the given statement is

If $a=0$ or $b=0$ then $ab=0$

Here, either $a=0$ or $b=0$

Then obviously $ab=0$

Therefore, the converse of the given statement is true.