$\"\"$

Statement :

(a)

If both $\"\"$ and $\"\"$ converges, then $\"\"$ converges.

Consider $\"\"$ , where $\"\"$ .

$\"\"$ is convergent.

$\"\"$ is convergent is convergent.

$\"\"$ is not convergent.

Therefore, the statement is false because $\"\"$ and $\"\"$ .

$\"\"$

Statement :

(b)

If $\"\"$ diverges, then $\"\"$ diverges.

The statement is correct because $\"\"$ .

By the comparision test if $\"\"$ diverges, then $\"\"$ diverges.

$\"\"$

(a) The statement is false.

(b) The statement is true.