1. SAT MATH Lesson 10

2. Drill Day 10 Identify each statement as True or False?
{2, 3, 5 } is a subset of {1, 2, 3, 4, 5, 6}
{0,3} is a subset of {1, 2, 3, 4}
{Maine} is a subset of {the New England States}
{college students} is a subset of {people studying calculus}
{0} is a subset of {0}
{o, 1, 2, 3, … , 9} is a subset of {all digits}
{rational numbers} is a subset of {real numbers}
{integers} is a subset of {whole numbers}
{odd integers} is a subset of {all prime numbers}
{triangles} is a subset of {polygons}

3. Sets
A set is any collection of objects, people of things that are carefully defined such as {American coins}, {one-digit prime numbers}, {even numbers}, {baseball players on a team} or {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Each object in a set is called a member or element of the set. The members of a set can be placed in brackets as a list or roster as {2, 4, 6, 8} or as a rule as in {the positive off integers less than 100}

4. Types of sets
A set is finite if the process of counting the set comes to an end. For example the finite set of two digit numbers can be written as {10, 11, 12, 13, … , 99} A set is infinite if the process of counting the set never comes to an end. For example the infinite set of whole numbers can be written as {0, 1, 2, 3, … } The empty set written as the symbol 0 or as with empty braces { } is a set that has no member. For example the set of integers between 7 and 8.

5. Subsets
If A = {0, 1, 2} then any set that contains only the elements from set A is said to be a subset of A. For example the following are subsets of A: {0}, {1}, {2}, {0,1}, {0,2}, {1, 2} , {0, 1, 2} and { } NOTE: {1, 2, 3} is call the improper subset of A but is nonetheless a subset The { } is a subset of all sets but itself.

6. Intersection
The intersection of two sets consists of the elements they have in common. For example if A = {2, 4, 6, 8, 10} and B = {3, 4, 5, 6, 7, 8} then the intersection of A and B would be {4, 6, 8} Using the symbol for intersection we can write: When two sets have no elements in common the sets are said to be disjoint.

7. Union
The union of two sets consists of the all of both sets with no common elements listed more than once. For example if A = {3, 5, 7} and B = {a, b, c, 5, 7, 9} then the union of A and B would be {a, b, c, 3, 5, 7 , 9} Using the symbol for intersection we can write: If A = {odd integers} and B = {even integers} then and { integers }