Final answer:
The student's question relates to divisibility rules for integers and how they apply to operations such as addition, subtraction, multiplication, but not universally to division.
Step-by-step explanation:
Understanding Divisibility of Integer Combinations
The question you've asked pertains to the fundamental divisibility rules within integers. Here's a concise explanation of each statement regarding integer divisibility:
- Statement a) If an integer a divides both b and c, then a also divides their sum (b + c).
- Statement b) Similarly, a divides the difference (b - c) of the two integers.
- Statement c) When a divides both b and c, it naturally divides their product (b * c).
- Statement d) The divisibility rule does not generally apply to division; that is, even if a divides b and c, it does not necessarily divide b / c, unless c is a multiple of a.
These rules help explain how the operations of addition, subtraction, and multiplication interact with divisibility but does not fully extend to division unless specific conditions are met.