Problem 348
Give a counterexample to show that each of the following generalization 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
Solution
a. 3 ÷ 6 has no integer equivalent.
b. 18 ÷ (1 + 2) = 6 but 18 ÷ 1 + 18 ÷ 2 = 27
c. 5 ÷ 1 = 5 but 1 ÷ 5 has no integer equivalent
d. 24 ÷ (2 + 6) = 3 but (24 ÷ 2) + 6 = 18 so both are not same.
e. 6 – (3 + 2) = 1 but (6 – 3) + 2 = 5, so both are not same
f. 3 – 2 = 1 but 2 – 3 = -1 , so both are not same.