Discussion and Examples
Example 1: Consider S = {A1, A2, A3} with
- A1 = {1, 2, 3}
- A2 = {1, 4, 5}
- A3 = {3, 5}.
A valid SDR would be {1, 4, 5}. (Note this is not unique: {2, 1, 3} works equally well, for example.)
Example 2: Consider S = {A1, A2, A3, A4} with
- A1 = {2, 3, 4, 5}
- A2 = {4, 5}
- A3 = {5}
- A4 = {4}.
No valid SDR exists; the marriage condition is violated as is shown by the subcollection {A2, A3, A4}.
Example 3: Consider S= {A1, A2, A3, A4} with
- A1 = {a, b, c}
- A2 = {b, d}
- A3 = {a, b, d}
- A4 = {b, d}.
The only valid SDR's are (c, b, a, d) and (c, d, a, b).
Read more about this topic: Hall's Marriage Theorem
Famous quotes containing the words discussion and/or examples:
“It was heady stuff, recognizing ourselves as an oppressed class, but the level of discussion was poor. We explained systemic discrimination, and men looked prettily confused and said: “But, I like women.””
—Jane O’Reilly, U.S. feminist and humorist. The Girl I Left Behind, ch. 2 (1980)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)