Test 1 Theorem List Flashcards Preview

TXST: Intro To Advanced Math > Test 1 Theorem List > Flashcards

Flashcards in Test 1 Theorem List Deck (32):
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 < 0

x • z < y • z

24

If x > y and z > 0

x + z > y
xz > yz

25

If x and y exist then either

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

26

If x > y and y > z

x > z

27

If x > 0 (inverses)

1/x > 0

28

If x > y (inverses)

1/x < 1/y

29

If x > 1

x^2 > x and x^2 > 1

30

If 0 < x < 1

x > x^2 and 1 > x^2

31

If x is not 0

x^2 > 0

32

If x < y

x < (x + y)/2 < y