Propositional Logic 3

Question 1

metavariables

Answer 1

expressions in meta-languages that represent arbitrary formulae

Question 2

when can a formula be neither a tautology or contradiction

Answer 2

when there is a combination of T and F in the output column

Question 3

in the WFF p ⇒ q, p is the p____?

Answer 3

premise

Question 4

in the WFF p ==> q, q is the c_______?

Answer 4

conclusion

Question 5

the implication symbol is ______ associative

Answer 5

right

Question 6

is the equivalence symbol associative?

Answer 6

yes

Question 7

is the conjunction symbol associative?

Answer 7

yes

Question 8

is the implication symbol associative?

Answer 8

NO

Question 9

describe the law of replication

Answer 9

p ⇒ q therefore i’m either not p or i’m q

Question 10

describe the contrapositive in words

Answer 10

the negation of the conclusion implies the negation of the premises

Question 11

each of the algebraic laws are in themselves a …?

Answer 11

tautology

Question 12

what is short-circuiting

Answer 12

skipping the evaluation of the second part of a boolean expression in a conditional statement if the first part is enough to determine the result

Question 13

benefit of short-circuiting

Answer 13

optimises and can speed up the execution of code

Question 14

disadvantage of short-circuiting

Answer 14

can cause unexpected problem if the right hand side of the short-circuited expression has a side effect that is important (but not executed)

Question 15

name of this algebraic law:

p ∨ q ⇔ q ∨ p

Answer 15

commutativity

Question 16

name of this algebraic law:

p ∧ (q ∨ r) ⇔ (p ∧ q) ∨ (p ∧ r)

Answer 16

distributivity

Question 17

name of this algebraic law:

⌐(p ∧ q) ⇔ ⌐p ∨ ⌐q

Answer 17

de Morgan’s Law

Question 18

name of this algebraic law:

⌐(⌐p) ⇔ p

Answer 18

double negation

Question 19

name of this algebraic law:

p ∧ true ⇔ p

Answer 19

tautology

Question 20

name of this algebraic law:

p ∨ true ⇔ true

Answer 20

tautology

Question 21

name of this algebraic law:

p ∨ false ⇔ p

Answer 21

contradiction

Question 22

name of this algebraic law:

p ∧ false ⇔ false

Answer 22

contradiction

Question 23

name of this algebraic law:

p ∨ (q ∨ r) ⇔ (p ∨ q) ∨ r

Answer 23

associativity

Question 24

name of this algebraic law:

p ∨ p ⇔ p

Answer 24

idempotence

Question 25

idempotence law with conjunction

Answer 25

p ∧ p ⇔ p

Question 26

idempotence law with disjunction

Answer 26

p ∨ p ⇔ p

Question 27

name of this algebraic law:

p ∨ ⌐p ⇔ true

Answer 27

law of the excluded middle

Question 28

name of this algebraic law:

p ∧ ⌐p ⇔ false

Answer 28

law of the excluded middle

Question 29

name of this algebraic law:

p ∧ (p ∨ q) ⇔ p

Answer 29

absorption law

Question 30

example of the absorption law

Answer 30

p ∨ (p ∧ q) ⇔ p

Question 31

name of this algebraic law:

(p ⇒ q) ⇔ (⌐p ∨ q)

Answer 31

implication law

Question 32

name of this algebraic law:

(p ⇒ q) ⇔ (⌐q ⇒ ⌐p)

Answer 32

contrapositive law

Question 33

name of this algebraic law:

(p ⇔ q) ⇔ (p ⇒ q) ∧ (q ⇒ p)

Answer 33

equivalence law

Question 34

imagine there are 4 shapes: a white circle, a white square, a black circle and a black square. let B be the proposition that the shape is black and C be the proposition that the shape is a circle. for which shape(s) is B ⇒ C false?

Answer 34

the black square

Question 35

why use inference rules rather than truth tables to prove the validity of a conclusion with premises containing many variables?

Answer 35

the size of truth tables grows exponentially

Question 36

if p ⇔ q is true under all interpretations, the propositions p and q are said to be…?

Answer 36

logically equivalent

Question 37

contradictions are said to be…?

Answer 37

unsatisfiable