DGD 9
        
(1) Equivalence relations:

 (1a) SE 7: #6

 (1b) Question: Define a relation on A = {0,1,2,...,8} as follows:

    a R b <-> a^2 is congruent to b^2 (mod 9)
    
    (i) Show that R is an equivalence relation on A.
    (ii) What is the partition of A defined by R?
    

(2) Counting

 (2a) SE 8: #10

 (2b) Let A and B be sets, |A|=3, |B|=7. Determine the number of 

    (i) all functions A->B
    (ii) injective functions A->B

(3) Principle of Inclusion-Exclusion: How many integers between 25 and 1000 (inclusive) are 

    (i) divisible by 3 or 5 (inclusive or);
    (ii) divisible by neither 3 nor 5;
    (iii) divisible by either 3 or 5 (but not both)?