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Discrete > Propositions > Flashcards

Propositions Flashcards

1
Q

Declarative statements that have a true or false value.

A

Proposition

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2
Q

Statements contingent upon indefinite values can be propositions.

A

False

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3
Q

“x = 1” is a proposition.

A

False

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4
Q

“Pigs can fly” is a proposition

A

True

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5
Q

Propositions are defined/denoted using the…

A

Triple bar symbol (≡)

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6
Q

logical operators that join simple propositions into a more complex one

A

Connectives

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7
Q

¬

A

Negation

(NOT · · ·)

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8
Q

∧

A

Conjunction

(· · · AND/BUT/YET · · ·)

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9
Q

∨

A

Disjunction

(· · · OR · · ·)

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10
Q

→

A

Implication

(IF · · · , THEN · · ·)

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11
Q

↔

A

Bi-Conditional

(· · · IF, AND ONLY IF, · · ·)

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12
Q

⊕

A

Exclusive Or

(· · · (English) OR · · ·)

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13
Q

(NOT · · ·)

A

negation (¬)

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14
Q

(· · · AND/BUT/YET · · ·)

A

conjunction (∧)

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15
Q

(· · · OR · · ·)

A

disjunction (∨)

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16
Q

(IF · · · , THEN · · ·)

A

implication (→)

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17
Q

(· · · IF, AND ONLY IF, · · ·)

A

bi-conditional (↔)

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18
Q

(· · · (English) OR · · ·)

A

exclusive or (⊕)

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19
Q

inverts the truth value of a proposition

A

negation (¬)

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20
Q

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

A

“Birds cannot sing”

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21
Q

combines the truth value of two propositions

A

conjunctions and disjunctions

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22
Q

A conjunction is only True, when both propositions are…

A

True

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23
Q

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

A

False

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24
Q

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

A

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

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25
Q

Conjunctions give a lot of information when…

A

True

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26
Q

A disjunction is ___, when at least one connected proposition is true

A

True

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27
Q

A disjunction is ___when both connected propositions are False

A

False

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28
Q

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

A

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

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29
Q

When both statements are True a disjunction is…

A

True

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30
Q

True ∧ False

A

False

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31
Q

True ∨ False

A

True

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32
Q

¬ False

A

True

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33
Q

False ∧ False

A

False

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34
Q

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

A

Implication

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35
Q

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

A

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”

36
Q

The two parts of an implication

A

pre-condition and post-condition

37
Q

A ___ behaves like a contract or promise

A

Implication or Conditional

38
Q

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

39
Q

A conditional is True when the pre-condition is…

40
Q

In regards to implication, ___ behaves conversely to “if”.

A

“only if”

41
Q

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

A

bi-conditional (↔)

42
Q

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

A

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

43
Q

requires that both statements are the same truth value

A

Bi-Conditional (↔)

44
Q

“English or”

A

Exclusive Or (⊕)

45
Q

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

A

Exclusive Or (⊕)

46
Q

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

A

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

47
Q

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

48
Q

Proposition Order of Operations

A
  1. Negation, 2. Conjunction, 3. Disjunction, 4. Implication, 5. Bi-Conditional/Exclusive Or
49
Q

False ∧ False ∨ True

50
Q

¬ False ∨ True

51
Q

¬ (False ∧ False) ∨ True

52
Q

True ∨ False → False

53
Q

True ∨ True → False

54
Q

True → True ∨ False

55
Q

True ↔ False ⊕ False

56
Q

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

57
Q

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

58
Q

Conditionals that have a False pre-condition are vacuously…

59
Q

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

60
Q

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

A

Equivalent

61
Q

In proofs, ___ can be substituted for each other.

A

Equivalent Statements

62
Q

The triple bar (≡) is used to denote…

A

Equivalent Statements

63
Q

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

A

the simple statements

64
Q

p ∧ p ≡ p

65
Q

q ∨ p ≡ p ∨ q

66
Q

q ∧ p ≡ p

67
Q

q ∨ p ≡ p

68
Q

¬ p ↔ q ≡ q ⊕ p

69
Q

¬ p → q ≡ q ∨ p

70
Q

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

A

Tautology (T)

71
Q

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

72
Q

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

A

Contradiction (F)

73
Q

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

74
Q

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

A

Contingent

75
Q

¬ p is contingent

76
Q

“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.

77
Q

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

A

Contingent

78
Q

p → p. Tautology, Contradiction, or Contingent?

79
Q

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

A

Contradiction

80
Q

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

A

Contingent

81
Q

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

82
Q

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

A

the number of simple statements

83
Q

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

A

alternate between true and false

84
Q

In a truth table, the first column top half…

A

is all true

85
Q

In a truth table, the first column bottom half…

A

is all false

Discrete (6 decks)

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