SOLUTION: Give a counterexample to show that each of the following generalizations about the set of integers is false: a. Closure property for division b. Distributive property for divis

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Question 451006: Give a counterexample to show that each of the following
generalizations about the set of integers is
false:
a. Closure property for division
b. Distributive property for division over addition
c. Commutative property for division
d. Associative property for division
e. Associative property for subtraction
f. Commutative property for subtraction
Thank you!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. -6/5, a division of two integers, does not produce an integer.
b. %28-5+%2B+3%29%2F4+=+-2%2F4+=+-1%2F2, not an integer.
c. 6%2F5%3C%3E5%2F6
d. %28a%2Fb%29%2Fc+=+a%2F%28bc%29, while a%2F%28b%2Fc%29+=+%28ac%29%2Fb, hence
%28a%2Fb%29%2Fc+%3C%3Ea%2F%28b%2Fc%29
e. (1-2)-3 = -1 - 3 = -4, whereas 1-(2-3) = 1--1 = 2.
f. 4-7 = -3, whereas 7-4 = 3.