Question

determine if each conjecture is true. if not, write or draw a counterexample. 24. points x, y, and z are coplanar. 25. if n is an integer, then -n is positive.

Explanation:

Step1: Analyze conjecture 24

In three - dimensional space, three non - collinear points always determine a plane. So, points \(X\), \(Y\), and \(Z\) are coplanar. This conjecture is true.

Step2: Analyze conjecture 25

Let \(n = 3\) (an integer). Then \(-n=-3\) which is negative. So, the conjecture "If \(n\) is an integer, then \(-n\) is positive" is false. A counter - example is \(n = 3\).

Answer:

1. True
2. False, counter - example: \(n = 3\)