Flashcards in Test 3 Theorem List Deck (20):

1

## A Relation

### Is any set of ordered pairs

2

## A function

### Is a set of ordered pairs such that no two pairs have the same first term

3

## The domain

### Is the set of elements that are the first term

4

## The range

### Is the set of elements that are the second element

5

## If A is a subset of D(f), then f(A)

### Is the set {f(x)|x is an element of A}

6

## If B is a subset of R(f), then the pre-image of B

### Is the set {x|f(x) is an element of B}

7

## If S is a subset of T and T is a subset of D(f), then

### f(S) is a subset of f(T)

8

## If W is a subset of V and V is a subset of R(f), then

### The pre-image of W is a subset of the pre-image of V

9

## If the union of S and T is a subset of D(f), then

### f(the union of S and T) = the union of f(S) and f(T)

10

## If the union of S and T is a subset of R(f), then

### The pre-image of the union of S and T = the union of the pre-image of S and the pre-image of T

11

## Definition of a Segment

### There exist real number a & b such that x is in the segment iff a < x < b

12

## Definition of an open set

### For each point p in the set S, there is a segment r such that p is in r and the r is a subset in S

13

## Suppose r and s are segments such that p is in their intersection, then

### The intersection of r and s is a segment

14

## If S and T is open, then

### Their union and intersection is open

15

## Definition of cluster point

### P is a cluster point of the set S if For each segment r containing p, there is an element q in S such that q is in r and q does not equal p

16

## Definition of closed sets

### S is closed if p is a cluster point of S and in S

17

## If S has exactly 1 element, then

### S is closed

18

## If S and T are closed, then

### Both their intersection and union are closed

19

## Suppose T is closed, then

### The compliment of T is open

20