Classify each of the following as true or false for whole numbers x and y. If false, show a counterexample.
a. If 7|x and 7
y, then 7
xy.
b. If d
(a + b), then d
a and d
b.
c. If d|(a + b) and d
a, then d
b.
d. If d|(x + y) and d| x, then d| y.
e. If 4
x and 4
y, then 4
xy.
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