Discrete Structures Quiz 1 Definitions

Question 1

proposition

Answer 1

a statement that is true or false

Question 2

look at examples and proofs and homeworks

Answer 2

:0

Question 3

truth value

Answer 3

of a proposition is T or F

Question 4

Logical variables

Answer 4

denoting propositions with letters

Question 5

negation

Answer 5

not
little corner p

Question 6

Principle of noncontradiction (PNC)

Answer 6

a proposition and its negation can be true at the same time

Question 7

conjunction

Answer 7

and

p ^ q

Question 8

disconjunction

Answer 8

or

p v q

Question 9

truth table

Answer 9

a logical variable is fully determined by its truth table

truth values of the operator if we are given the truth value of p and q

Question 10

conditional

Answer 10

p -> q

if p then q

Question 11

vacuously true

Answer 11

in conditionals, the assumption is F so whole propositions is vacuously true

Question 12

biconidtional

Answer 12

p <-> q

or

p->q ^ q->p

Question 13

exclusive or

Answer 13

only one can be true

p (circle with + inside) q

Question 14

equivalence

Answer 14

2 logical operators are equivalent if they have the same truth tables

<=> or = with three lines

Question 15

building p and q in the truth tables

Answer 15

half t of the previous one

Question 16

contrapositive

Answer 16

p -> q
=(with 3 lines)
not q -> not p

Question 17

1st de morgan law

Answer 17

not (p ^ q)
= with three lines
not p v not q

Question 18

2nd de morgan law

Answer 18

not (p v q)
= with 3 lines
not p ^ not q

Question 19

binary expressions

Answer 19

compare the corresponding one

Question 20

tautology

Answer 20

compound propositions that is always true

Question 21

contradiction

Answer 21

compound proposition that is always false

Question 22

contingency

Answer 22

compound proposition that is neither true or false

Question 23

argument

Answer 23

an assertion that gives some propositions p1…pn imply another proposition q

Question 24

premises

Answer 24

p1..pn, propositions that imply a conclusion

Question 25

conclusion

Answer 25

q
being implied by the premises

Question 26

notation for arguments

Answer 26

p1…pn |-> q
OR
p1
…
pn
—-
three dots q

Question 27

valid

Answer 27

an argument is valid whenever all premises are true

Question 28

fallacy

Answer 28

premises are true but conclusion is false

Question 29

theorem (of arguments)

Answer 29

an argument p1…pn three dots q is valid if and only if p1^…^pn ->q is always T

Question 30

modus ponens

Answer 30

p ->q
p
—
three dots q

Question 31

hypothetical syllogism

Answer 31

p->q
q->r
—
three dots p-> r

Question 32

modus tollens

Answer 32

p->q
not q
—
therefore not p

Question 33

propositional functions

Answer 33

predicates

have a domain and P(x)
where P(x) is the output as a propositions

Question 34

universal quantifier

Answer 34

V-
for all

Question 35

existential quantifier

Answer 35

E backwards
there is OR there exists

Question 36

uniqueness quantifiers

Answer 36

E!
e is backwards

there is a unique

Question 37

1st de morgan law for quantifiers

Answer 37

not (V-x, P(x))
= with three lines
Ex, P(x)
e is backwards

Question 38

2nd de morgan law for quantifiers

Answer 38

not (Ex, P(x))
e is backwards
= with three lines
V- x, not P(x)