theory quiz

Question 1

a ‘is in” b symbol

Answer 1

not defined

Question 2

A is a subclass of B symbol

Answer 2

A “symbol” B -> for all x:x in A -> x in B

Question 3

empty set symbol

Answer 3

{} = {x:x not equal to x}

Question 4

{a,b}

Answer 4

{x: x=a v x=b}

Question 5

{a}

Answer 5

{x:x=a}

Question 6

{a1, a2…an}

Answer 6

{x: x=a1 v x=a2…}

Question 7

UA

Answer 7

{x:x in y for some y in A}

Question 8

AUB

Answer 8

U{A,B}

Question 9

nA

Answer 9

{x:x in y for all y in A}

Question 10

AnB

Answer 10

n{A,B}

Question 11

(a,b)

Answer 11

{{a},{b}}

Question 12

(a1…an)

Answer 12

((a1…an-1), an)

Question 13

AxB

Answer 13

{(a,b): a in A ^ b in B}

Question 14

A1x…An

Answer 14

{(a1…an): ai in Ai for a=1…n}

Question 15

PA

Answer 15

{x: x subclass A}

Question 16

A^c

Answer 16

{x:x not in a}

Question 17

A\B

Answer 17

{x:x in A ^ x not in B}

Question 18

Function

Answer 18

in f and in f, then y=z

Question 19

relation

Answer 19

binary relation R on A is a subset of AxA

Question 20

dom f

Answer 20

{x:(x,y) in f for some y}

Question 21

axiom of extensionality

Answer 21

A=B iff (for all x x in A iff x in B)

Question 22

axion of empty set

Answer 22

The empty set is a set

Question 23

axiom of pairing

Answer 23

for all objects a,b the class {a,b} is a set

Question 24

axiom of subset

Answer 24

if B subclass A and A is a set, then B is a set

Question 25

axiom of union

Answer 25

If A is a set, then UA is a set

Question 26

axiom of power

Answer 26

If A is a set, then PA is a set

Question 27

axiom of infinity

Answer 27

There exists z a set s.t. the empty set is in z and if a in z, then au{a} in z

Question 28

axiom of replacement

Answer 28

if f is a function, if dom f is a set, then ran f is a set

Question 29

axiom of choice

Answer 29

Cartesian product of a collection of non-empty sets is non-empty

Question 30

ran f

Answer 30

{fx:x in dom f}

Question 31

f:A->B

Answer 31

f is a function with A=domf ranf subclass of B

Question 32

f(x)

Answer 32

f is a function, x in dom f and (x, f(x)) in f

Question 33

Ui Ai

Answer 33

union of all sets Ai indexed by I=Uf[I]

Question 34

ni Ai

Answer 34

n{Ai: i in I}

Question 35

{x in A: P(x)}

Answer 35

set of all elements of A satisfying property P