unit 6 logic

Question 1

empty set

Answer 1

∅ or { }

Question 2

⊆

Answer 2

subset

Question 3

A⊂B

Answer 3

proper subset, if A⊆ B but A≠ B

Question 4

A–B

Answer 4

x:x∈ A and x∉B

Question 5

power set

Answer 5

set of all subsets of S, { T: T⊆ S}.

Question 6

cardinality

Answer 6

number of (distinct) elements in S

Question 7

proposition

Answer 7

an expression with a truth value(TRUEor FALSE).

Question 8

WFF of propositional logic

Answer 8

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

Question 9

Satisfiable WFF

Answer 9

If there is an interpretation in which the WFF is true

Question 10

Tautology (WFF)

Answer 10

When WFF is true in every interpretation

Question 11

Contradiction (WFF)

Answer 11

When WFF is false in every interpretation

Question 12

Contingent (WFF)

Answer 12

When WFF is true in some and false in other

Question 13

Logically equivalent (WFF)

Answer 13

Same truth value

Question 14

argument consists of?

Answer 14

premises and a conclusion

Question 15

argument is valid if

Answer 15

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

Question 16

predicate

Answer 16

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

Question 17

universal quantifier∀

Answer 17

denotes “all”, “every”, or“any”

Question 18

existential quantifier∃

Answer 18

some”, “exists”, or “there is”

Question 19

∀X.loves(X, adele)

Answer 19

Everyone loves Adele

Question 20

∃X.loves(adele, X)

Answer 20

Adele loves someone.

Question 21

Well-formed formulae of predicate logic

Answer 21

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

Question 22

Atomic formula

Answer 22

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

Question 23

bound variable

Answer 23

a variable that occurs within the scope of a quantifier

Question 24

free variable

Answer 24

a variable that appears outside the scope of a quantifier

Question 25

sentence of predicate logic

Answer 25

a WFF in which every variable is bound

Question 26

SQL

Answer 26

SELECT columns FROM table WHERE condition

Question 27

countable

Answer 27

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

Question 28

countably infinite

Answer 28

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

Question 29

uncountable

Answer 29

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