Parallelism
Let be a set of all pairs of lines in a given plane such that .
Which option is valid for this questions in all cases?
Note: In this problem, a line is not parallel to itself.
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1 solution
The answer to this question may seem equivalence at first, but it is actually if x = y .
It is an reflexive because, then we are telling that one line is parallel to itself. But, they are one and the saame line. And according to the definition of parallel lines, two lines with different coordinates should have the same inclination with the horizontal, but they have same corrdinates. So, it is not refledive.
Now, as it is not reflexive, there is no chance for this relation to be equivalence.
Now, lets check for transitive. If x is related to y such that they are parallel lines and y is related to x such that they are parallel lines, then x should be related to x such that they are parallel lines. But they are one and the same line, so they are not parallel as explained above. So, even though this question has wide chances for beg transitive, it is not because it does not saisfy this type of relation.
So, the final answer is that this relation is symmetric .