1. Prove that A(BC)=(AB)(AC) Section 1.2 2. Let R={(a,b),(a,c),(c,d),(a,a),(b,a)}. What is RR, the composition of R with itself? What is R1, the inverse of R ? Is R,RR, or R1 a function? Section 1.3 3. Let R and S be the binary relations on A={1,,7} with the graphical representations shown in Figure 1. (a) Indicate whether each of R and S is (i) symmetric, (ii) reflexive, and (iii) transitive. (b) Repeat (a) for the relation RS. 4. Let RAA be a binary relation as defined below. In which cases is R a partial order? a total order? (a) A= the positive integers; (a,b)R if and only if b is divisible by a. (b) A=N;(a,b)R if and only if b=a or b=a+1