Check all statements that are true. a. Adding two integers and then taking the remainder produces the same result as taking their remainders first, then adding them, and then applying the remainder operation once more.
b. Saying that a divides b is the same as saying that b is a multiple of a.
c. Adding two integers and then taking the remainder produces the same result as taking their remainders first and then adding them.
d. When you perform division by 5 with remainder, the remainder is an integer from -5 to 5.
e. If an integer a divides a product of two integers b and c, then a must divide b or a must divide c.
f. If an integer divides two numbers, it also divides their difference.
g. If an integer divides two numbers, it also divides their sum.
h. When you perform division by 3 with remainder, the remainder is one of the integers 0,1,2.
i. If a and b are positive integers, and a = bq + r is the decomposition of a given by the division algorithm, then q can be found as the floor of a/b, and then r can be found as r = a - bq.
j. If an integer a divides an integer b, then a also divides any multiple of b.