Flashcards in Test 1 Theorem List Deck (33):

1

## Set

### a collection of all things

2

## Elements

### Contents of a set

3

## Definition of a Union

### x is in A union B iff x is in A or B

4

## Definition of an Intersection

### x is in A intersect B iff x is in A and B

5

## Definition of A subset B

### If x is in A, then x is in B

6

## Definition of Set Equality

### A is a subset of B and B is a subset of A

7

## Definition of a Compliment

### The compliment of A is all elements not in A

8

## If A is a subset of B, and B is a subset of C

### A is a subset of C

9

## If A is a subset of B

### A intersect B equals A

10

## If A is a subset of C, and B is a subset of C

### A intersect B is a subset of C

11

## If A is a subset of B, and A is a subset of C

### Then A is a subset of B intersect C

12

## If A intersect B is a subset of A intersect C, and A union B is a subset of A union C

### B is a subset of C

13

## The compliment of A intersect B equals

### The compliment of A union the compliment of B

14

## The compliment of A union B equals

### The compliment of A intersect the compliment of B

15

## If x and y are positive

### x + y is positive and x • y is positive

16

## Definition of a positive number

### x is positive, x is 0, is -x is positive

17

## x • y is positive iff

### x and y have the same signs

18

## Definition of greater than

### x = y + c

19

## x is positive iff

### x > 0

20

## If x > y (addition)

### x + z > y + z

21

## If x > y (negatives)

### -y > -x

22

## If x > 0 (negatives)

### 0 > -x

23

## If x > y and z exists

### x • z > y • z

24

## If x > y and z < 0

### x • z < y • z

25

## If x > y and z > 0

### x + z > y

26

## If x and y exist then either

### x = y, x > y, or x < y

27

## If x > y and y > z

### x > z

28

## If x > 0 (inverses)

### 1/x > 0

29

## If x > y (inverses)

### 1/x > 1/y

30

## If x > 1

### x^2 > x and x^2 > 1

31

## If 0 < x < 1

### x > x^2 and 1 > x^2

32

## If x is not 0

### x^2 > 0

33