1. I took a shower so I cleaned the room.

2. I took a shower, so I cleaned the room.
3. I took a shower so that I cleaned the room.

(What does #1 mean? Does it mean #2 or #3?)

4. I took a raincoat so I might wear it when it rained.

5. I took a raincoat, so I might wear it when it rained.

6. I took a raincoat so that I might wear it when it rained.

(Does #4 mean #5 or #6?)

1 and 2 mean the same; 3 does not.

4, 5, and 6 all mean the same.