Determine if each statement is true or false. If the statement is false, explain why, or show work proving that it is false.

a. If a = 5, then ac = 5c.

b. If ac = 5c, then a = 5.

a). true

b). true

Step-by-step explanation:

a).

Given : If a = 5, then ac = 5c

Let c be any constant.

a = 5 (given)

Therefore, ac = 5c

Here a is given a constant value (5), also let assume c to be a constant. So when we multiply each term we will get a constant value of 5c. The ratio does not change.

Hence proved.

b).

Given : If ac = 5c, then a = 5

Let c be any constant

It is given, a = 5

Therefore, ac = 5c

Here the product of two terms is given as 5c, where c is assume to be a constant. Then as a product rule, the value of a will be 5. The ratio will not change.

Hence proved.