- #1

- 81

- 0

Attempt: I don't understand that if R2 has elements nothing to do with the elements of R1, how can an R2 class be a union of those elements belonging to an R1 class?

- Thread starter bedi
- Start date

- #1

- 81

- 0

Attempt: I don't understand that if R2 has elements nothing to do with the elements of R1, how can an R2 class be a union of those elements belonging to an R1 class?

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 961

It is, of course, possible that the two relations are

But in this case the "if and only if" statement says

- #3

- 81

- 0

- #4

- 35,220

- 6,307

The usual way to proceed is to do one direction at a time: first, suppose R1 is a subset of R2 and deduce that every R2-class is the union of R1 classes; next, suppose every R2-class is the union of R1 classes and deduce that R1 is a subset of R2.

Commonly, either or both of these might most easily be achieved by working backwards. E.g. for the first half above, suppose some R2-class is not a union of R1 classes, then show there's an element of R1 that is not in R2. (With all this logical negation and reversal going on, the trap to avoid is proving the same direction twice over.)

- Replies
- 0

- Views
- 1K

- Replies
- 1

- Views
- 2K

- Replies
- 0

- Views
- 1K

- Replies
- 2

- Views
- 4K

- Replies
- 3

- Views
- 975

- Replies
- 1

- Views
- 790

- Last Post

- Replies
- 3

- Views
- 970

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 3K