Discrete Structures Week 3

Question 1

Argument

Answer 1

an assertion that given some propositions P1…Pn (premises) imply another propositions q (conclusion)

P1..Pn |-> q
P1..Pn three dots q

Question 2

valid

Answer 2

q is true whenever P1…Pn are all true

Question 3

Fallacy

Answer 3

invalid, premises are true, conclusion is false

Question 4

Theorem - about arguments

Answer 4

an argument P1…Pn |-> q is valid if and only if P1^P2^…^Pn |-> q is a tautology

Question 5

3 Standard rules of inferences

Answer 5

Modus Ponens

hypothetical syllogism

Modus Tollens

Question 6

Modus Ponens

Answer 6

p -> q
p
—-
three dots q

is valid

Question 7

Hypothetical Syllogism

Answer 7

p -> q
q -> r
—
three dots r

is valid

Question 8

Two methods prove theorems

Answer 8

truth tables or apply theorem with assumptions

Question 9

Modus Tollens

Answer 9

p -> q
not q
—-
three dots not p

is valid

Question 10

What is a propositional function

Answer 10

has a domain of what we can input
variables
predicate - kinda like the function

Question 11

universal qualifier

Answer 11

V- (dash through the middle)

for all

Question 12

uniqueness qualifier

Answer 12

E!
backwards E

there is a unique

Question 13

existential qualifier

Answer 13

E, backwards

there is or there exists

Question 14

multiple function inputs

Answer 14

L(x,y) = “x likes y”
domain: set of all people
can use the qualifiers to manipulate the function examples on one note

Question 15

1st de morgan’s law for quantifiers

Answer 15

not ( V-x, P(x)) <-> E(back)x, not P(x)

Question 16

2nd de morgan’s law

Answer 16

not (E(back)x, p(x)) <-> V-x, not p(x)

Question 17

set and notation

Answer 17

an unordered collection of objects(elements)
- a set is said to contain elements

x C- S
- x is an element a set S

x C-| S
- x is not an elements in set S