HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
Here's a problem I came up with many years ago:
Give two sets P and Q such that
1) P and Q are completely contained in the square \(\displaystyle -1\le x\le 1\), \(\displaystyle -1\le y\le 1\).
2) P contains the diagonally opposite points (-1, -1) and (1, 1).
3) Q contains the diagonally opposite points (-1, 1) and (1, -1).
4) P and Q are both connected sets.
5) \(\displaystyle P\cap Q\) is empty.
Give two sets P and Q such that
1) P and Q are completely contained in the square \(\displaystyle -1\le x\le 1\), \(\displaystyle -1\le y\le 1\).
2) P contains the diagonally opposite points (-1, -1) and (1, 1).
3) Q contains the diagonally opposite points (-1, 1) and (1, -1).
4) P and Q are both connected sets.
5) \(\displaystyle P\cap Q\) is empty.