ALGEBRA II HONORS/GIFTED @ ALGEBRA II HONORS/GIFTED - SETS : THE COMPLEMENT OF A SET and CROSS PRODUCTS ALGEBRA II HONORS/GIFTED @ SETS : THE COMPLEMENT OF A SET and CROSS PRODUCTS

U U = {students at Chiles} A = {students in this class} A 1) What can you say about the region inside U, but not in set A? COMPLEMENT : of a set are the elements in U, but not in the specified set . Complements are noted using the symbols A’ or .

ROSTER METHOD : a way to write the elements of a set by listing all of the elements. RULE METHOD : a way to write the elements of a set by definition. Let : U = {1, 2, 3, 4, …, 20} J = {2, 4, 6, 8, …, 20} K = {2, 3, 5, 7, 11, 13, 17, 19} L = {1, 3, 9, 11} 2) Each set above is described using the roster method. Describe the same sets using the rule method. 3) Find the complement of sets J, K, and L. 4) Draw a Venn Diagram of sets U, J, K, and L.

SUBSET : if all of the elements in set A are also in set B. Explain why… 5) 6) A set is a subset of itself. 7) U A B

9) Name all subsets of {r, a, t}. ALGEBRA II HONORS/GIFTED - SETS : THE COMPLEMENT OF A SET and CROSS PRODUCTS 8) If S = {students in this class}, name some subsets of S. Name a set which is not a subset of S. 9) Name all subsets of {r, a, t}.

If A = {1, 2} and B = {a, b, c}, then A x B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} This is known as a CROSS PRODUCT. What is the cross product of two sets? If A and B are two sets, the cross product of A and B, written A×B, is the set of all pairs wherein the first element is a member of the set A and the second element is a member of the set B. 10) So, what is B x A?

C = {gobbling, gobbled, goblins} and D = {gargoyles, gobbling}. 11) Find C x D if C = {gobbling, gobbled, goblins} and D = {gargoyles, gobbling}. C x D = {(gobbling, gargoyles), (gobbling, gobbling), (gobbled, gargoyles), (gobbled, gobbling), (goblins, gargoyles), (goblins, gobbling)}