DGD 8
        
        

(1) Composition of functions: review the definition
        
    Question: Let f: A -> B and g: B ->C be two functions. Is each of the following statements true?
    If so, prove it; otherwise, give a counterexample.
        
    (i) if g is not injective, then g*f (composition) is not injective.
    (ii) if f and g are both surjective, then g*f is surjective
        

(2) The floor function assigns to any real number the largest integer less than or equal to it,
    i.e. it rounds down to the nearest integer.
    Its domain is the set of real numbers, and its codomain is the set of integers.
    Is this function injective? surjective? Sketch its graph.
        

(3) Properties of relations: review the definitions of reflexive, symmetric, antisymmetric, transitive
    SE 6: #5 (R1, R2, R4 only), #1, #7a, #6a, #4ac


(4) Equivalence relations: review the definition of an equivalence relation,
    define an equivalence class.
    SE 7: #2