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- Inequalities for proposition 3 in question 4?
- nx < ny - 1
- For some m, m-1 < ny ≤ m
- So ny - 1 ≤ m - 1
- Section 7.2
- Recall the family relationships
- Henry VII married Elizabeth of York, and had children
- Arthur
- Margaret
- Henry VIII
- Arthur married Katherine of Aragon
- Henry VIII married Katherine of Aragon, and had child
- Mary
- Henry VIII married Anne Boleyn, and had child
- Elizabeth I
- Henry VIII married Jane Seymour, and had child
- Edward VI
- Henry VIII married Anne of Cleves
- Henry VIII married Katherine Howard
- Henry VIII married Katherine Parr
- Henry VII married Elizabeth of York, and had children
- Find a reflexive relation on these people…
- …For which someone suggests “has the same spouse as”
- Which is indeed reflexive if we exclude people whose spouses aren’t in the relevant set of people
- And it’s actually symmetric and transitive too
- So this relation is an equivalence relation
- Note that the properties of the relation depend on the set it’s defined on as well as on the rule that defines it
- For example, if we hadn’t excluded people with no spouses, “same spouse” wouldn’t be reflexive
- And if we added a second wife for Arthur (Anne the Imaginary), “same spouse” would no longer be transitive
- Equivalence classes
- Read section 7.3