metalogic and set theory

Question 1

the study of logical systems

Answer 1

metalogic

Question 2

any argument we can formally prove is valid

Answer 2

soundness

Question 3

we can formally prove any tautologically valid argument
- if an argument is formally provable in BOOL, then the argument is valid

Answer 3

completeness

Question 4

true or false: if a conclusion, C, is provable in a formal proof from some premises, then those premises entail C.

Answer 4

true

Question 5

the ability to express any possible truth function

Answer 5

truth function completeness (not the same as completeness)

Question 6

what are the things in the set?

Answer 6

elements or members

Question 7

true or false: sets can have other sets as elements

Answer 7

true

Question 8

set builder notation

Answer 8

{Ax: x is prime}

Question 9

set member relation

Answer 9

weird E

Question 10

how do you say “a is a member of b”?

Answer 10

a E b

Question 11

3 rules of sets

Answer 11

1. order doesn’t matter
2. repetition doesn’t matter
3. name choice doesn’t matter

Question 12

how do you represent the empty set?

Answer 12

{} or /O

Question 13

number of elements in the set

Answer 13

cardinality
|a|

Question 14

|N|

Answer 14

infinite number aleph naught