Propositional Logic 2

Question 1

describe - in words - the only time that ‘p ⇒ q’ is false

Answer 1

when the antecedent is true but the consequence is false

Question 2

‘if’ mid-sentence corresponds to…?

Answer 2

⇐

Question 3

‘only if’ corresponds to….?

Answer 3

⇒

Question 4

If the lecturer hadn’t shown up last week, Plato would have
given the lecture.

Answer 4

¬S ⇒ P

Question 5

Exactly one of the following happened: David won or
Victoria won or it was a tie.

Answer 5

(D ∧ ¬V ∧ ¬T ) ∨ (V ∧ ¬D ∧ ¬T ) ∨ (T ∧ ¬D ∧ ¬V )

Question 6

In the context of the implication p ⇒ q, p is referred to as the…?

Answer 6

premise

Question 7

In the context of the implication p ⇒ q, q is referred to as the…?

Answer 7

conclusion

Question 8

difference between a proposition and a formula

Answer 8

propositions are the declarative statements. formulae use propositional variables to represent propositions and/or their relationships with one another

Question 9

what are the 2 types of formulae…?

Answer 9

atomic and compound

Question 10

atomic formulae do not contain any…?

Answer 10

propositional connectives

Question 11

what are the 2 components of atomic formulae…?

Answer 11

the two truth constants (true and false) and propositional variables

Question 12

another word for equivalence

Answer 12

biconditionality

Question 13

compound formulae

Answer 13

formulae (compound or atomic) linked by connectives

Question 14

order of precedence of the 5 propositional connectives

Answer 14

⌐, ∧, ∨, ⇒, ⇔

Question 15

if an expression contains multiple propositional connectives of the same order of precedence, operations are evaluated from…?

Answer 15

right to left

Question 16

in syntax trees, the leaf nodes are…?

Answer 16

the propositional variables

Question 17

in syntax trees the parent nodes are…?

Answer 17

the propositional connectives

Question 18

the root of the syntax tree

Answer 18

the propositional connective that was applied last

Question 19

a set of propositions is consistent when…?

Answer 19

it is logically possible for all propositions to be true at the same time

Question 20

consistency vs validity | deals with…?

Answer 20

the coexistence of propositions vs the relationship between premises and conclusion in an argument.

Question 21

consistency vs validity | applies to…?

Answer 21

a set of propositions or statements vs arguments composed of premises and a conclusion

Question 22

the capital latter ‘P’ wou;d refer to the

Answer 22

Propositional statement

Question 23

how to express XOR in propositional logic

Answer 23

p ⇔ ¬q (or similarly q ⇔ ¬p)

Question 24

NAND connective symbol

Answer 24

p| q

Question 25

NOR connective symbol

Answer 25

p ↓ q

Question 26

how to express a NAND relationship in propositional logic

Answer 26

¬(p ∧ q)

Question 27

how to express a NOR relationship in propositional logic

Answer 27

¬(p ∨ q)

Question 28

synonym for formula

Answer 28

well formed formula

Question 29

is P, the propositional variable, also a propositional formula? why/why not?

Answer 29

yes - propositional variables are SIMPLE propositional formulae

Question 30

syntax trees make it clear how the expression should be ________.

Answer 30

parsed