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Flashcards in unit 6 logic Deck (29)
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1

empty set

∅ or { }

2

subset

3

A⊂B

proper subset, if A⊆ B but A≠ B

4

A–B

x:x∈ A and x∉B

5

power set

set of all subsets of S, { T: T⊆ S}.

6

cardinality

number of (distinct) elements in S

7

proposition

an expression with a truth value(TRUEor FALSE).

8

WFF of propositional logic

any of:
a propositional variable
not A
A intersection B
A union B
if A then B, 1101

9

Satisfiable WFF

If there is an interpretation in which the WFF is true

10

Tautology (WFF)

When WFF is true in every interpretation

11

Contradiction (WFF)

When WFF is false in every interpretation

12

Contingent (WFF)

When WFF is true in some and false in other

13

Logically equivalent (WFF)

Same truth value

14

argument consists of?

premises and a conclusion

15

argument is valid if

there is no interpretation in which the premises are TRUE and the conclusion is FALSE

16

predicate

a property of some object x or the relationship between two or more objectsx, y, etc., written p(x), p(x, y), etc.

17

universal quantifier∀

denotes “all”, “every”, or“any”

18

existential quantifier∃

some”, “exists”, or “there is”

19

∀X.loves(X, adele)

Everyone loves Adele

20

∃X.loves(adele, X)

Adele loves someone.

21

Well-formed formulae of predicate logic

A WFF of propositional logic is: given a set of constant, variable or predicate symbols a WFF is:
an atomic formula
a WFF of propositional logic
∀v.A where v is a variable symbol and A is a WFF
∃v.A where v is a variable symbol and A is a WFF

22

Atomic formula

p(t1,t2..tn) where p is a predicate symbol of arity n and each of t1..tn is a constant symbol or variable symbol

23

bound variable

a variable that occurs within the scope of a quantifier

24

free variable

a variable that appears outside the scope of a quantifier

25

sentence of predicate logic

a WFF in which every variable is bound

26

SQL

SELECT columns FROM table WHERE condition

27

countable

if and only if it can be placed in a one-to-one correspondence with some subset of the natural numbersℕ= {1, 2, 3, ...}

28

countably infinite

if and only if it can be placed in a one-to-one correspondence with the set of natural numbers

29

uncountable

if noone-to-one correspondence with the natural numbers is possible.