Model Answer:

Let a=6, b=15, c=30

a and b both divide 30.

However, ab=90 does not divide 30.

Thus, statement at (a) is obviously not always true.

If a and b are relatively prime, it is obvious to see that ab shall divide c.

If a and b are prime numbers, obviously they are relatively prime if they are different.

Hence the result follows.

Thus, (b) & (c) are correct answers.

But for (c) to be true, we need to assume that a and b are not same numbers.

For precise proof of statement at (b), refer to any standard book of Number Theory,