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(Solved): * EXERCISE \( \quad \) 2.4.4: Showing a statement is true or false by direct proof or counterexamp ...



* EXERCISE \( \quad \) 2.4.4: Showing a statement is true or false by direct proof or counterexample.
Determine whether the s(m) If \( x, y \), and \( z \) are integers and \( x \mid(y+z) \), then \( x \mid y \) or \( x \mid z \).
(n) If \( x, y \),

* EXERCISE \( \quad \) 2.4.4: Showing a statement is true or false by direct proof or counterexample. Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (m) If \( x, y \), and \( z \) are integers and \( x \mid(y+z) \), then \( x \mid y \) or \( x \mid z \). (n) If \( x, y \), and \( z \) are integers such that \( x \mid(y+z) \) and \( x \mid y \), then \( x \mid z \). (o) If \( x \) and \( y \) are integers and \( x \mid y^{2} \), then \( x \mid y \).


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