Posted by m on .
Give a counterexample to show that each of the following generalizations about the set of integers {3,2,1,0,1,2,3} is false.
a) closure property for division
b) distributive property for division over addition.

math 
MathMate,
a. Closure property for division means that the result of the division of numbers in the given set belongs to the set.
For example, for the set {1,1}, the closure for division is true, because (1/1)=1, and (1/1)=1. So all possible divisions of numbers in the set yield a result also in the set.
For the set {1,2}, closure for division is not true. Although 2/1=1 is in the set, 1÷2 = 1/2 is not in the set. So 1÷2 is a counter example of closure.
Try to figure out a few counter examples, and post if you have doubts.
b. Distributive property of multiplication over addition is the following:
5*(2+3)=5*2+5*3=25
Does this work for division?
5/(2+3)=? 5/2 + 5/3 = 25/6 = 4 1/6
The preceding example is a counter example of the distributive property for division over addition.