Question:
If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true? [Page No. 7]
Answer:
Verified
Yes, the claim is true. The points (x, y) and (y, x) are equal if and only if x = y.
If x ≠ y, then the coordinates are in a different order, so the points are different. If x = y, both ordered pairs become (x, x) and represent the same point.
Therefore, (x, y) = (y, x) exactly when x = y.
