TABLE 1 Set Identities. Identity Name AnU = A Identity laws AUØ = A AUU = U AnØ = Ø Domination laws AUA = A AnA = A Idempotent laws (A) = A Complementation law AUB = BUA Commutative laws AnB = BOA AU (BU C) = (A U B) U C An (Bn C) = (A n B)nC Associative laws AU (Bn C) = (A U B) n (A U C) An (BU C) = (A n B) U (An C) Distributive laws AOB = AUB AUB = AnB De Morgan's laws AU (An B) = A Absorption laws An (AU B) = A AUĀ = U A NĀ= Ø Complement laws

2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?

This Venn diagram represents areas for students who like different subjects in all combinations   List all areas (in an ascending order) that represent students who like the following:(For example for students who like History you need to put 4,5,6,7 No spaces between symbols.) a) like Math only   b)  like English and History   c)  Do not like Math   d)  Like Math or History   e)  Like English and History, but do not like Math   f)  Like Math or English, but do not like History

21. Show that if A and B are sets, then a) AB=An B. b) (An B) U (An B) = A.

Show that:a) Every element of A belongs to some equivalence class.b) Two elements are equivalent if and only if their equivalence classes are equalc) Two equivalence classes are either identical or they are disjoint.

5) Suppose a path C is defined by r(t), 2 and r(8)= . If f is a differentiable function satisfying f(3,9) = 6 and f(6, 10) = 14, what is the value of Vf dr?

Suppose set A = {green, blue, red} and set B = {gray, purple, blue} (a) What is A ∪ B? (b) What is A ∩ B?