Definitions

Question 1

Modus Ponens

Answer 1

If A, then B. A, so B.

Question 2

Modus Tollens

Answer 2

If A, then B. Not B, so not A.

Question 3

Double-negation elimination (DNE)

Answer 3

Not not A, so A.

Question 4

Disjunctive syllogism (DS)

Answer 4

A or B. Not A, so B.

Question 5

Syntax

Answer 5

Vocabulary and grammatical rules.

Question 6

Semantics

Answer 6

Meaning.

Question 7

Logical consequence

Answer 7

If B is a logical consequence of A, then B follows from A; if A is true then B is true.

Question 8

Derivability

Answer 8

Syntactic validity.

Question 9

Entailment

Answer 9

Semantic validity.

Question 10

Counter-example

Answer 10

Situation in which the premises are all true, but the conclusion is false.

Question 11

Contradiction

Answer 11

Proposition that is never true.

Question 12

Satisfiable

Answer 12

Proposition that can be true.

Question 13

Tautology

Answer 13

Proposition that is always true.

Question 14

Logically equivalent

Answer 14

When two propositions have the same truth value in every situation. (A is a logical consequence from B and vice versa).

Question 15

Arbitrary

Answer 15

Random.

Question 16

⊨ ϕ

Answer 16

Proposition ϕ is a tautology.

Question 17

≡

Answer 17

Logically equivalent.

Question 18

∧

Answer 18

And.

Question 19

In a valid inference, if we have true premises…

Answer 19

then we must have a true conclusion.

Question 20

In a valid inference, if we have a true conclusion…

Answer 20

then the premises can be either true or false.

Question 21

In a valid inference, if we have false premises…

Answer 21

then the conclusion can be either true or false.

Question 22

In a valid inference, if we have a false conclusion…

Answer 22

then we must have false premises.

Question 23

Middle term

Answer 23

The predicate that is contained in both of the premises.

Question 24

Domain of discourse

Answer 24

Square

Question 25

Collectives

Answer 25

'not', 'and', 'or'.

Question 26

Classical quantifiers

Answer 26

'all', 'some', 'no'.

Question 27

Other quantifiers

Answer 27

'most', 'many'

Question 28

Monotonicity

Answer 28

Assertion (declaration) stays true when we change predicates, upward (Dutch-->European) or downward (all men-->male tax payers).