6. Show the following equivalences either using Venn Diagram or using transformation using various laws (2 points each) 8 points total b) complement (A U B) complement(A) complement(B) (De Morgan's law of sets) c) (A-B)-C = (A-B) n (A-C) d) A U (B C) (A U B) (A U C) (Distributive Law of sets) Section 2.3 Functions - (20 points total + 4 points bonus) 7. Determine whether f is a function from Z (integer domain) to R (real number domain) (2 points each) a) f(n)- n. b) f(n) = square-root (n2+ 1) c) f(n)-1/(n2 4). 8. Let S 1,0, 2,4, 7. Find f(S) for the following cases. Note that f(S) maps (one point each) - total 4 points (a) f(x)-1 for Vx E S (b) f(x) 2x +1 for VxES (c) f(x)-ceiling (x/5) for VxES (d) f(x)-floor((x2 + 1)/3) for V xES 9. Find f g and g o f, where f(x) = x2 + 1 and g(x) = x + 2, are functions from R to R. [ 2 points eachl