Math 325K Assignment 7 Due Oct. 27 at 11:00 am 1 Cardinality rules Prove the following, where A and B are finite sets. a) |A B| = |A| |B| b) |A B| = |A| + |B| |A B| 2 Relations and identity Let R be a binary relation between A and B. Recall that IdA and IdB are the identity relations on A and B (e.g. a1 IdA a2 if and only if a1 = a2 ). The following four statements are equivalent (in some order) to \"R is surjective,\" \"R is injective,\" \"R is total,\" and \"R is a partial function.\" Which is which? a) R R1 IdB b) R R1 IdB c) R1 R IdA d) R1 R IdA 3 Counting usernames A website has the following rules for usernames: they must be between 4 and 6 characters long, the first character must be an uppercase letter (i.e. 'A' through 'Z'), and the following characters must be letters or numbers (i.e. 'A' through 'Z', 'a' through 'z', and '0' through '9'). How many total usernames are possible? 1