**Example 1**:

Write down two implications based on the following statement.

*y*

^{3}= -125 if and only if

*y*= -5.

**:**

SolutionSolution

Implication 1: If

*y*^{3}= -125, then*y*= -5.Implication 2: If

*y*= -5, then*y*^{3}= -125.**Example 2**:

Write down two implications based on the following statement.

8 is a factor of 24 if and only if 24 can be divided exactly by 8.

**:**

SolutionSolution

Implication 1: 8 is a factor of 24 if 24 can be divided exactly by 8.

Implication 2: 24 can be divided exactly by 8 if 8 is a factor of 24.

**Example 3**:

State the converse of the following statement and hence, determine whether its converse is true or false.

(a) If 2*x*> 8, then

*x*> 4.

(b) If

*x*is a multiple of 6, then it is a multiple of 3.

**:**

SolutionSolution

(a) Converse implication: If

*x*> 4, then 2*x*> 8. The converse is true.

(b) Converse implication: If

*x*is a multiple of 3, then it is multiple of 6. The converse is false. (9 is a multiple of 3 but it is not a multiple of 6)