Propositional Logic 1

Question 1

natural language

Answer 1

a language used for normal everyday communication

Question 2

formal language

Answer 2

a set of strings of symbols formed from a finite alphabet and defined by specific rules

Question 3

4 examples of rules that can be used to define formal languages

Answer 3

regular expressions, regular grammar, context-free grammar, context-sensitive grammar

Question 4

natural language is inherently…?

Answer 4

ambiguous

Question 5

premises

Answer 5

a proposition used in an argument to prove the truth of the conclusion

Question 6

formal languages have no invalid…?

Answer 6

inferences

Question 7

programming language

Answer 7

a formal constructed language designed to communicate instructions to a machine to control its behaviour

Question 8

propositional logic is a type of…?

Answer 8

formal system

Question 9

a formal system is a formal language equipped with a…?

Answer 9

consequence operation/deduction rule/inference rule

Question 10

inference rules

Answer 10

logical tools used to draw conclusions from premises

Question 11

inference rules form the foundation of…?

Answer 11

logical reasoning

Question 12

propositional

Answer 12

a logical statement that can either be true or false but NOT both

Question 13

atomic proposition

Answer 13

a logical statement that is either true or false (but not both) and cannot be broken down any further

Question 14

compound propositions state…?

Answer 14

relationships between propositions

Question 15

compound proposition

Answer 15

a proposition combining multiple propositions using logical connectives

Question 16

defining languages involves at least…?

Answer 16

two languages

Question 17

what are the two fundamental languages required for defining languages

Answer 17

the object language and the meta-language

Question 18

object language

Answer 18

the language being defined

Question 19

meta-language

Answer 19

the language used to define an object language

Question 20

an object language has how many aspects?

Answer 20

2

Question 21

aspects of an object language

Answer 21

its syntax and semantics

Question 22

syntax

Answer 22

rules for writing an object language

Question 23

semantics

Answer 23

the meanings of constructions in an object language

Question 24

defining syntax involves how many steps?

Answer 24

2

Question 25

step 1 in defining syntax

Answer 25

defining the symbols

Question 26

step 2 in defining syntax

Answer 26

defining larger constructions (e.g. sentences in NLs and formulae in propositional logic)

Question 27

propositional variables represent...?

Answer 27

atomic propositions

Question 28

names for propositional variables are often...?

Answer 28

abbreviations of the proposition

Question 29

propositional variables tend to be...?

Answer 29

lower case

Question 30

purpose of propositional connectives

Answer 30

form compound propositions from multiple simpler propositions

Question 31

each logical connective has its own...?

Answer 31

semantics

Question 32

p ∧ q 'p' and 'q' can be referred to as the...?

Answer 32

conjuncts

Question 33

p ∨ q 'p' and 'q' can be referred to as the...?

Answer 33

disjuncts

Question 34

law of excluded middle

Answer 34

for every proposition, either the proposition or its negation is true

Question 35

why is the 'law of excluded middle' named as such?

Answer 35

every truth value is either true of false since there is no middle ground when it comes to the truth of a propositional formula

Question 36

p ⇒ q is equivalent to...?

Answer 36

¬q ⇒ ¬p

Question 37

¬q ⇒ ¬p is equivalent to...?

Answer 37

p ⇒ q

Question 38

the contrapositive of p ⇒ q

Answer 38

¬q ⇒ ¬p

Question 39

WFF stands for

Answer 39

well-formed formulae

Question 40

law for equivalence

Answer 40

(p ⇒ q) ∧ (q ⇒ p)

Question 41

number of steps in the process of logical deduction

Answer 41

3

Question 42

step 1 in the process of logical deduction

Answer 42

identify the premises (true propositions)

Question 43

step 2 in the process of logical deduction

Answer 43

construct and inference from the premises

Question 44

step 3 in the process of logical deduction

Answer 44

give a conclusion

Question 45

what is a conclusion

Answer 45

the process of giving some new proposition a truth value

Question 46

if p and (p ⇒ q) are both true, then it can be inferred that...?

Answer 46

q is true as well

Question 47

what is 'q if p' written using propositional logic?

Answer 47

p ⇒ q

Question 48

what is 'q whenever p' written using propositional logic?

Answer 48

p ⇒ q

Question 49

what is 'p only if q' written using propositional logic?

Answer 49

p ⇒ q

Question 50

describe the equivalence law in words.

Answer 50

the conjuncts are proposition and its converse

Question 51

p ⇒ ¬q is equivalent to

Answer 51

q ⇒ ¬p

Question 52

technical term for ¬

Answer 52

negation

Question 53

the law of the excluded middle is associated with which propositional connective?

Answer 53

disjunction

Question 54

the process of defining syntax has how many step..?

Answer 54

2

Question 55

what is the first step in defining syntax?

Answer 55

defining the basic symbols

Question 56

what is the second step in defining syntax?

Answer 56

defining the rules for writing formulae with these symbols