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TERM 1
Equal Sets
DEFINITION 1 A and B are sets. If A and B contain, or do not contain, the same points, then A and B are equal. TERM 2
Subsets
DEFINITION 2 A and B are sets. If x is a point in A and x is a point in B; then A is a subset of B. TERM 3
Theorem
DEFINITION 3 If A and B are sets and A is equal to B, then A is a subset of B and B is a subset of A. TERM 4
Theorem
DEFINITION 4 If A and B are sets and A is a subset of B and B is a subset of A; then A is equal to B. TERM 5
Intersection
DEFINITION 5 A and B are sets. The set C is the intersection of A and B means that is x is a point in C, then x is a point in A and x is a point in B.
TERM 6
Union
DEFINITION 6 A and B are sets. The set D is the union of A and B means that is x is a point contained in D, then x is a point in A or x is a point in B. TERM 7
Theorem
DEFINITION 7 If A, B, C are sets, then the intersection of A and the union of B and C is equal to the union of the intersection of A and B and the intersection of A and C TERM 8
Theorem 2.
DEFINITION 8 If A and B and U are sets, and 1.) if A is a subset of B, the complement of B is a subset of the complement of A, and 2.)id the complement of B is a subset of the complement of A, then A is a subset of B. TERM 9
Theorem 2.
DEFINITION 9 If A,B, and U are sets, then the complement of the union of A and B is equal to the intersection of complement of A and the complement of B. TERM 10
R
DEFINITION 10 R1 is the set of all real numbers with their natural ordering. There is a 1-1 correspondence between the set of real numbers and the set of points on a horizontal line directed from left to right.
