4.4 Implications (Sample Questions)


Example 1:
Write down two implications based on the following statement.
y3 = -125 if and only if y = -5.

Solution
:

Implication 1: If y3 = -125, then y = -5.
Implication 2: If y = -5, then y3 = -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.

Solution
:

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 2x > 8, then x > 4.
(b) If x is a multiple of 6, then it is a multiple of 3.

Solution
:

(a) Converse implication: If x > 4, then 2x > 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) 

Leave a Reply

Your email address will not be published. Required fields are marked *