Propositional Logic

Question 1

A statement that is either true or false

Answer 1

Proposition

Question 2

~

Answer 2

not

Answer 3

and

Question 4

v

Answer 4

or

Question 5

–>

Answer 5

If-Then

Answer 6

If and only if

Question 7

IFF

Answer 7

If and only if

Either both are true or both are false

Question 8

Bent Hyphen Symbol

Answer 8

Not

Alternatively, line over letter

Question 9

Logical equivalent

Answer 9

The truth values of two statements are the same

Question 10

Contrapositive

Answer 10

The negative of a statement

If p implies q, not q implies not p.

Question 11

Converse

Answer 11

The reverse implication of a statement

P implies Q
Converse: Q implies P

Question 12

An implication & its converse together are equivalent to what?

Answer 12

An IFF statement

Question 13

The purpose of Truth tables

Answer 13

Assign truth values to propositional symbols & compound statements

Question 14

De Morgan’s Law

Answer 14

Distributes a negative to a conjunction or disjunction

Question 15

Tautology

Answer 15

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

Question 16

Contradiction

Answer 16

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

Question 17

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

Answer 17

Therefore: propositions that involve all numbers have special set notation

Question 18

Upside down A

Answer 18

For all

Question 19

N

Answer 19

For the set of non-negative integers

Question 20

E

rounded

Answer 20

Is a member of
Belongs to
Is in

Question 21

Critical rows

Answer 21

The rows of a truth table where all premises are true

Question 22

Validity

Answer 22

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

Question 23

Predicate

Answer 23

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

Question 24

Predicate notation

Answer 24

Similar to functional notation:

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

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

Question 25

A universally quantified statement

Answer 25

An assertion that a predicate is always true

Question 26

An existentially quantified statement

Answer 26

An assertion that a predicate is sometimes true

Question 27

Upside down Ax E D, P(x)

Answer 27

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

Question 28

Reverse Ex D, P(x)

Answer 28

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

Question 29

Modus Ponens

Answer 29

p p --> q q - The cornerstone of deductive reasoning If the antecedent of a conditional is true, then the consequent must also be true.

Question 30

Modus Tollens

Answer 30

p --> q ~q ~p If the consequent of a conditional is false, then the antecedent must also be false.

Question 31

Satisfiable

Answer 31

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

Question 32

Disjunctive addition

Answer 32

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

Question 33

Conjunctive simplification

Answer 33

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

Question 34

Disjunctive Syllogism/ Disjunctive Inference

Answer 34

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

Question 35

Hypothetical Syllogism | Chain Rule

Answer 35

A rule of inference pertaining to If/Then operator. Given two conditionals, you can chain the conclusion. p --> q q --> r p --> r

Question 36

Proof by contradiction

Answer 36

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

Question 37

Division into Cases

Answer 37

- List the Cases - Give proof a proposition holds for each case - conclude the overall proposition holds p v q p --> r q --> r r

Question 38

Affirming the Consequent

Answer 38

Converse error, Confusion of necessity and sufficiency Inferring the converse from the original statement p --> q q p

Question 39

Denying the Antecedent

Answer 39

Inverse error Inferring the inverse from the original statement p --> q ~p ~q

Question 40

``` Other Popular Sets: 0 struck through Z Q C ```

Answer 40

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