math
posted by m
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.

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.
Respond to this Question
Similar Questions

math
Give a counterexample to show that the following generalization about the set of integers is false. Closure property for division. 
math
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) commutative property for subtraction b)associative property for subtraction 
math
TRUE OR FALSE (x+y)+2=2+(x+y) is it associative property? 
Algebra 2
Need help PLEASE!! Question is: There is no Closure Property of Division that applies to Integers. For example 2 divided by 3 is not an interger. What is another example of real numbers that does not have a Closure Property for one … 
mat
In some cases the Distributive Property of Multiplication over Addition or Distributive Property of Multiplication over Subtraction can be used to obtain an answer quickly. Represent the following operations using one of the distributive … 
math
Write an algebraic expression that requires each of the following properties of real numbers to simplify, in the order given: the Distributive Property, the Associative Property of Addition, the Commutative Property of Addition, and … 
Geometry
Complete the twocolumn proof. Given: x/5 + 9 = 11 Prove: x = 10 x/5 + 9 = 11 a.__________ x/5 = 2 b.__________ x = 10 c.__________ A) a. Given b. Subtraction Property of Equality c. Division Property of Equality B) a. Given b. Subtraction … 
Algebra2
Name the property of real numbers for 2(x+4)=2x8 associative property of multiplication communitive property of addition distributive property associate property of addition my answer is distributive property 
Math 1
1. Justify the solution to (x5)=56+6(x5) by matching a property to each step. Step 1: 4(X5)=56 Step 2: X5=14 Step 3: X=9 A addition property of equality B subtraction property of equality C multiplication property of equality … 
geometry
Name the property of equality or congruence that justifies going from the first statement to the second statement. StartFraction x Over 2 EndFraction equals 3x2=3 x equals 6x=6 symmetric property of congruencesymmetric property of …