I need some help double checking my work and the teacher likes to obfuscate his answers.
I am negating the given statements regardless of whether they are true or false.
1: Given a line and a point not on the line, there exists a line parallel to the given line through the given point.
My Answer:
There exist some line A and some point Q not on A, such that there does not exist a line parallel to A through Q.
2:Given a line and a point not on the line, there exists a unique line parallel to the given line through the given point.
My Answer:
There exist some line A and some point Q not on the line A, such that there does not exist a unique line parallel to line A through point Q.
Best Answer
Negation of first statement made by you is correct and for statement 2 the negation can be like following: 1. There exist some line A and some point Q not on the line A, such that there does not exist any line parallel to line A through point Q.
2.There exist some line A and some point Q not on the line A, such that there does exist more than one line parallel to line A through point Q.
Here both the above statements can be used as negation of the $2^{nd}$ statement provided by you.