Assignment:
One of the most often misunderstood concepts in math is divisibility. Divisibility is a different operation than division and the two are often confused.
The solution describes the seven key properties of divisibility and proves them mathematically to show the reader that they are true and why they are important.
The seven divisibility properties are as follows:
(a) a|0, a|a
(b) a|1 if and only if a = ±1
(c) if a|b and c|d, then ac|bd (for c?0)
(d) if a|b and b|c, then a|c (for b?0)
(e) (a|b and b|a) if and only if a = ±b
(f) if a|b and b?0, then |a|?|b|
(g) if a|b and a|c, then a|(bx+cy) for any integers x,y.
Provide complete and step by step solution for the question and show calculations and use formulas.