Quiz 1

Question 1

A set whose elements can be listed in a sequence

Answer 1

Countable set

Question 2

A countable set

Answer 2

Discrete set

Question 3

The study of discrete (i.e. countable) objects and the relationship between them

Answer 3

Discrete mathematics

Question 4

Consists of a new vocabulary word together with its description using already known terms

Answer 4

Definition

Question 5

A declarative sentence that is both true or false, but not both

Answer 5

Proposition (a statement)

Question 6

A sequence of sentences demonstrating the truth of a claim

Answer 6

Argument (a proof)

Question 7

OR (∨)
AND (∧)
Negation/ NOT (~)
Implication implies/ if-then (→)
If and only if (⇔)

Answer 7

Logical operators (connectives)

Question 8

Two propositional forms p and q are ________ if and only if they have the same truth values for each possible substitution of propositions into their component propositional variables

Answer 8

Logically equivalent

Question 9

Theorem:
~(p ∨ q) ≡ ~p ∧ ~q
~(p ∧ q) ≡ ~p ∨ ~q

Answer 9

DeMorgan’s Law

Question 10

A propositional form that is always true, denoted t

Answer 10

Tautology

Question 11

A propositional form that is always false, denoted c

Answer 11

Contradiction

Question 12

p ∧ q ≡ q ∧ p
p ∨ q ≡ q ∨ p

Answer 12

Commutative Law

Question 13

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Answer 13

Associative Law

Question 14

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Answer 14

Distributive Law

Question 15

p ∧ t ≡ p
p ∨ c ≡ p

Answer 15

Identity Law

Question 16

p ∨ ~p ≡ t
p ∧ ~p ≡ c

Answer 16

Negation Law

Question 17

~(~p) ≡ p

Answer 17

Double Negation Law

Question 18

p ∧ p ≡ p
p ∨ p ≡ p

Answer 18

Idempotent Law

Question 19

p ∨ t ≡ t
p ∧ c ≡ c

Answer 19

Universal bound

Question 20

p ∨ (p ∧ q) ≡ p
p ∧ (p ∨ q) ≡ p

Answer 20

Absorption Law

Question 21

~t ≡ c
~c ≡ t

Answer 21

Negation of t and c

Question 22

p ∨ q → r ≡ (p → r) ∧ (q → r)

Answer 22

Division into cases

Question 23

p → q ≡ ~p ∨ q

Answer 23

Theorem 1

Question 24

Negating p → q:
~(p → q) ≡ p ∧ ~q

Answer 24

Theorem 2

Question 25

p → q ≡ ~ q → ~p

Answer 25

Contrapositive

Question 26

p → q ≢ q → p

Answer 26

Converse

Question 27

p → q ≡ ~p → ~q

Answer 27

Inverse

Question 28

q → p

Answer 28

p if q

Question 29

“If not q, then p”, which by contraposition is logically equivalent to p → q

Answer 29

p only if q

Question 30

≡ (p → q) ∧ (q → p)
≡ (~p ∨ q) ∧ (~q ∨ p)

Answer 30

p ⇔ q

Question 31

“If not p, then not q”, which by contraposition is logically equivalent to q → p

Answer 31

Necessary

Question 32

“If p, then q”

Answer 32

Sufficient

Question 33

≡ (p ∨ q) ∧ (~p ∧ ~q)

Answer 33

p ⊕ q

Question 34

An argument where every case the premise is proven true, the conclusion is also true

Answer 34

Valid Argument