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Discrete > Propositional Logic > Flashcards

Propositional Logic Flashcards

1
Q

A statement that is either true or false

A

Proposition

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2
Q

~

A

not

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3
Q
A

and

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4
Q

v

A

or

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5
Q

–>

A

If-Then

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6
Q
A

If and only if

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7
Q

IFF

A

If and only if

Either both are true or both are false

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8
Q

Bent Hyphen Symbol

A

Not

Alternatively, line over letter

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9
Q

Logical equivalent

A

The truth values of two statements are the same

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10
Q

Contrapositive

A

The negative of a statement

If p implies q, not q implies not p.

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11
Q

Converse

A

The reverse implication of a statement

P implies Q
Converse: Q implies P

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12
Q

An implication & its converse together are equivalent to what?

A

An IFF statement

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13
Q

The purpose of Truth tables

A

Assign truth values to propositional symbols & compound statements

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14
Q

De Morgan’s Law

A

Distributes a negative to a conjunction or disjunction

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15
Q

Tautology

A

A logical statement that is always true, regardless of the truth values of its variables

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16
Q

Contradiction

A

A logical statement that is always false, regardless of the truth values of the variables in it.

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17
Q

You can’t check a claim about an infinite set by checking a finite set of its elements

A

Therefore: propositions that involve all numbers have special set notation

18
Q

Upside down A

A

For all

19
Q

N

A

For the set of non-negative integers

20
Q

E

rounded

A

Is a member of
Belongs to
Is in

21
Q

Critical rows

A

The rows of a truth table where all premises are true

22
Q

Validity

A

The conclusion is true no matter what truth values are assigned to individual propositional variables

23
Q

Predicate

A

A proposition whose truth depends on the value of one or more variables

24
Q

Predicate notation

A

Similar to functional notation:

P(n) ::= n is a perfect square

P(n) is either true or false depending on the value of n.

25
Q

A universally quantified statement

A

An assertion that a predicate is always true

26
Q

An existentially quantified statement

A

An assertion that a predicate is sometimes true

27
Q

Upside down Ax E D, P(x)

A

For all x in D, P(x) is true

28
Q

Reverse Ex D, P(x)

A

There exists an x in D such that P(x) is true

29
Q

Modus Ponens

A

p
p –> q
q

  • The cornerstone of deductive reasoning

If the antecedent of a conditional is true, then the consequent must also be true.

30
Q

Modus Tollens

A

p –> q
~q
~p

If the consequent of a conditional is false, then the antecedent must also be false.

31
Q

Satisfiable

A

A proposition is satisfiable if some setting of the variables makes the proposition true.

32
Q

Disjunctive addition

A

A rule of inference pertaining to OR

Add any statement, true or false, to a true statement

p
p v q

Valid because a disjunction is true if at least one of its statements is true

33
Q

Conjunctive simplification

A

A rule of inference pertaining to AND

In a given true conjunction, any conjunct can be separated out and is true.

p^q
p, q

34
Q

Disjunctive Syllogism/ Disjunctive Inference

A

A rule of inference pertaining to OR

In a disjunction, if one disjunct is false, the other has to be true.

“The process of elimination”

p v q
~q
p

35
Q

Hypothetical Syllogism

Chain Rule

A

A rule of inference pertaining to If/Then operator.

Given two conditionals, you can chain the conclusion.

p –> q
q –> r
p –> r

36
Q

Proof by contradiction

A

To prove something, assume the converse & arrive at a contradiction.

37
Q

Division into Cases

A
  • List the Cases
  • Give proof a proposition holds for each case
  • conclude the overall proposition holds

p v q
p –> r
q –> r
r

38
Q

Affirming the Consequent

A

Converse error,
Confusion of necessity and sufficiency

Inferring the converse from the original statement

p –> q
q
p

39
Q

Denying the Antecedent

A

Inverse error

Inferring the inverse from the original statement

p –> q
~p
~q

40
Q 
Other Popular Sets:
0 struck through
Z
Q
C
A

Empty set
Integers (Z)
Rational Numbers (Q)
Complex Numbers (C)

Discrete (2 decks)

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