Propositions

Question 1

Declarative statements that have a true or false value.

Answer 1

Proposition

Question 2

Statements contingent upon indefinite values can be propositions.

Answer 2

False

Question 3

“x = 1” is a proposition.

Answer 3

False

Question 4

“Pigs can fly” is a proposition

Answer 4

True

Question 5

Propositions are defined/denoted using the…

Answer 5

Triple bar symbol (≡)

Question 6

logical operators that join simple propositions into a more complex one

Answer 6

Connectives

Question 7

¬

Answer 7

Negation

(NOT · · ·)

Question 8

∧

Answer 8

Conjunction

(· · · AND/BUT/YET · · ·)

Question 9

∨

Answer 9

Disjunction

(· · · OR · · ·)

Question 10

→

Answer 10

Implication

(IF · · · , THEN · · ·)

Question 11

↔

Answer 11

Bi-Conditional

(· · · IF, AND ONLY IF, · · ·)

Question 12

⊕

Answer 12

Exclusive Or

(· · · (English) OR · · ·)

Question 13

(NOT · · ·)

Answer 13

negation (¬)

Question 14

(· · · AND/BUT/YET · · ·)

Answer 14

conjunction (∧)

Question 15

(· · · OR · · ·)

Answer 15

disjunction (∨)

Question 16

(IF · · · , THEN · · ·)

Answer 16

implication (→)

Question 17

(· · · IF, AND ONLY IF, · · ·)

Answer 17

bi-conditional (↔)

Question 18

(· · · (English) OR · · ·)

Answer 18

exclusive or (⊕)

Question 19

inverts the truth value of a proposition

Answer 19

negation (¬)

Question 20

Suppose p ≡ “Birds can sing”, then ¬p ≡

Answer 20

“Birds cannot sing”

Question 21

combines the truth value of two propositions

Answer 21

conjunctions and disjunctions

Question 22

A conjunction is only True, when both propositions are…

Answer 22

True

Question 23

A conjunction is False when at least one connected proposition is…

Answer 23

False

Question 24

Suppose p ≡ “Birds can sing”, and q ≡ “Travis likes bagels”, then p ∧ q ≡ …

Answer 24

p ∧ q ≡ “Birds can sing, and Travis likes bagels”

Question 25

Conjunctions give a lot of information when...

Answer 25

True

Question 26

A disjunction is \_\_\_, when at least one connected proposition is true

Answer 26

True

Question 27

A disjunction is \_\_\_when both connected propositions are False

Answer 27

False

Question 28

Suppose p ≡ “I like bagels”, and q ≡ “My name isn’t Travis”, then p ∨ q ≡ ...

Answer 28

“I like bagels, or my name isn’t Travis”

Question 29

When both statements are True a disjunction is...

Answer 29

True

Question 30

True ∧ False

Answer 30

False

Question 31

True ∨ False

Answer 31

True

Question 32

¬ False

Answer 32

True

Question 33

False ∧ False

Answer 33

False

Question 34

\_\_\_, or conditions (→), are frequently used in mathematics.

Answer 34

Implication

Question 35

p ≡ “You did your chores” q ≡ “You went to the park” p → q ≡ ...

Answer 35

p → q ≡ “If you did your chores, then you went to the park”, or p → q ≡ “You did your chores, implies you went to the park”

Question 36

The two parts of an implication

Answer 36

pre-condition and post-condition

Question 37

A ___ behaves like a contract or promise

Answer 37

Implication or Conditional

Question 38

A conditional is always True when the post-condition is...

Answer 38

True

Question 39

A conditional is True when the pre-condition is...

Answer 39

False

Question 40

In regards to implication, ___ behaves conversely to "if".

Answer 40

"only if"

Question 41

The ___ connective is used when implication holds in both directions.

Answer 41

bi-conditional (↔)

Question 42

p ≡ “I studied”, q ≡ “I passed”, p ↔ q ≡ ...

Answer 42

p ↔ q ≡ “I studied, if and only if, I passed.”

Question 43

requires that both statements are the same truth value

Answer 43

Bi-Conditional (↔)

Question 44

"English or"

Answer 44

Exclusive Or (⊕)

Question 45

is True when exactly 1 of the 2 statements are True.

Answer 45

Exclusive Or (⊕)

Question 46

p ≡ “I studied”, q ≡ “I failed”, p ⊕ q ≡ ...

Answer 46

“I studied, or I failed, but not both.”

Question 47

When both statements are True, then the “exclusive or” is

Answer 47

FALSE

Question 48

Proposition Order of Operations

Answer 48

1. Negation, 2. Conjunction, 3. Disjunction, 4. Implication, 5. Bi-Conditional/Exclusive Or

Question 49

False ∧ False ∨ True

Answer 49

TRUE

Question 50

¬ False ∨ True

Answer 50

TRUE

Question 51

¬ (False ∧ False) ∨ True

Answer 51

TRUE

Question 52

True ∨ False → False

Answer 52

FALSE

Question 53

True ∨ True → False

Answer 53

FALSE

Question 54

True → True ∨ False

Answer 54

TRUE

Question 55

True ↔ False ⊕ False

Answer 55

TRUE

Question 56

A conditional can be made ___ by ensuring that the pre-condition is False

Answer 56

TRUE

Question 57

A conditional can be made True by ensuring that the pre-condition is...

Answer 57

FALSE

Question 58

Conditionals that have a False pre-condition are vacuously...

Answer 58

TRUE

Question 59

Conditionals that have a False pre-condition are ___ True.

Answer 59

vacuously

Question 60

Statements that have identical truth values for every possible assignment of truth-values for the simple statements are called...

Answer 60

Equivalent

Question 61

In proofs, ___ can be substituted for each other.

Answer 61

Equivalent Statements

Question 62

The triple bar (≡) is used to denote...

Answer 62

Equivalent Statements

Question 63

Statements that have identical truth values for every possible assignment of truth-values for ____ are called Equivalent.

Answer 63

the simple statements

Question 64

p ∧ p ≡ p

Answer 64

TRUE

Question 65

q ∨ p ≡ p ∨ q

Answer 65

TRUE

Question 66

q ∧ p ≡ p

Answer 66

FALSE

Question 67

q ∨ p ≡ p

Answer 67

FALSE

Question 68

¬ p ↔ q ≡ q ⊕ p

Answer 68

TRUE

Question 69

¬ p → q ≡ q ∨ p

Answer 69

TRUE

Question 70

a statement that results in True for all truth-value assignments of the simple statements

Answer 70

Tautology (T)

Question 71

A Tautology, T, is a statement that results in ___ for all truth-value assignments of the simple statements.

Answer 71

TRUE

Question 72

a statement that results in False for all truth-value assignments of the simple statements.

Answer 72

Contradiction (F)

Question 73

A Contradiction, F, is a statement that results in ___ for all truth-value assignments of the simple statements.

Answer 73

FALSE

Question 74

A statement is ___ if it is neither a Tautology nor a Contradiction.

Answer 74

Contingent

Question 75

¬ p is contingent

Answer 75

TRUE

Question 76

“To Be ∨ ¬ To Be” is a ___ because regardless of whether “To Be” is True or False at least one piece in the “or” is True.

Answer 76

tautology

Question 77

¬ p → p. Tautology, Contradiction, or Contingent?

Answer 77

Contingent

Question 78

p → p. Tautology, Contradiction, or Contingent?

Answer 78

Tautology

Question 79

¬ p ∧ (p ∨ p). Tautology, Contradiction, or Contingent?

Answer 79

Contradiction

Question 80

¬ p ∧ (q ∨ p). Tautology, Contradiction, or Contingent?

Answer 80

Contingent

Question 81

p → (p ∨ q). Tautology, Contradiction, or Contingent?

Answer 81

Tautology

Question 82

In a truth table, the number of combinations/rows is 2^N, where N is...

Answer 82

the number of simple statements

Question 83

In a truth table, the last column of the simple statments will...

Answer 83

alternate between true and false

Question 84

In a truth table, the first column top half...

Answer 84

is all true

Question 85

In a truth table, the first column bottom half...

Answer 85

is all false