M3_Predicate Logic and Proof Techniques

Question 1

Important in proving if arguments are valid or not and it is being used to represent knowledge

Answer 1

Propositional Logic

Question 2

• Evaluates to true or false
  
  • Takes one or more arguments
  • Expresses a predicate involving argument(s)
  • Becomes a PROPOSITION when values are assigned to the arguments

Answer 2

Propositional function

Question 3

• An extension of Propositional Logic
  
  • Adds the concept of predicates and quantifiers to better capture the meaning of statements that cannot adequately expressed by propositional logic

Answer 3

Predicate logic

Question 4

Using quantifiers to create such propositions

Answer 4

QUANTIFICATION

Question 5

Two types of quantifier

Answer 5

Universal Quantifier
Existential Quantifier

Question 6

A set of unvirse

Answer 6

domain of discourse

Question 7

Symbol for universal quantifier

Answer 7

Inverted A

Question 8

Symbol for Existential Quantifier

Answer 8

Horizontally inverted E

Question 9

important for conducting proofs and program verification but also for artificial intelligence

Answer 9

mathematical reasoning

Question 10

• Sequence of statements that form an argument

Answer 10

Proof

Question 11

sets of statements

Answer 11

Rules of interference

Question 12

incorrect reasoning

Answer 12

fallacies

Question 13

• A basic assumption about mathematical structure that needs no proof because it is accepted as true and correct

Answer 13

Axiom

Question 14

• used to create new concepts in terms of existing ones

Answer 14

Definition

Question 15

• Proposition that has been proved to be true
• proved by logical arguments based on axioms

Answer 15

Theorem

Question 16

• A minor auxiliary result which aids in the proof of a theorem/proposition

Answer 16

LEMMA

Question 17

• a result whose proof follows immediately from a theorem or proposition

Answer 17

Corollary

Question 18

• is a statement that is suspected to be true by experts but not yet proven

Answer 18

Conjecture

Question 19

Every even integer greater than 2 can be expressed as the sum of two prime numbers.

Answer 19

Goldbach’s Conjecture

Question 20

if p is true then q must follow

Answer 20

Proof by construction or Direct Proof

Question 21

prove p->q by proving ~q->~p

Answer 21

Proof by Contraposition

Question 22

prove that the negation of the theorem yields a contradiction

Answer 22

proof by contradiction