Logic & Reasoning

Question 1

Types of Argument in mathematical Reasoning

Answer 1

Deductive and Inductive Reasoning

Question 2

Structure: moving from general premise to specific conclusion

Answer 2

Deductive reasoning

Question 3

All dogs are animals, so my dog is an animal.

Answer 3

Deductive Reasoning

Question 4

Structure: specific premise to general conclusion

Answer 4

Inductive reasoning

Question 5

Strength: If the premise is true, conclusion is more likely to be true (but could be false)

Answer 5

Inductive Reasoning

Question 6

May be used to visually evaluate the validity of a deductive argument

Answer 6

Euler Diagram

Question 7

Applies when a conditional and its antecedent are given as premises, and the consequent is the conclusion.

Answer 7

Law of Detachment (Modus Ponens- mode that affirms)

Question 8

The general form for Law of Detachment is ___

Answer 8

Premise: p implies q
Premise p
Conclusion: q

Question 9

When a conditional and the negation of its consequent are given as premises, and the negation of its antecedent is the conclusion.

Answer 9

Law of Contraposition (Modus Tollens- mode that denies)

Question 10

Arises when a conditional and its consequent are given as premises, and the antecedent is the conclusion.

Answer 10

Fallacy of the Converse

Question 11

General form of Law of Contraposition

Answer 11

Premise: p implies q
Premise: ~q
Conclusion: ~p

Question 12

General form of Fallacy of a Converse

Answer 12

Premise: p implies q
Premise: q
Conclusion: p

Question 13

Occurs when a conditional and the negation of its antecedent are given as premises, and the negation of the consequent is the conclusion.

Answer 13

Fallacy of the Inverse

Question 14

General from of Fallacy of the Inverse

Answer 14

Premise: p implies q
Premise: ~p
Conclusion: ~q

Question 15

A complete declarative sentence P(x) involving variable x.

Answer 15

Propositional Function (Predicate)

Question 16

In a Propositional Function or Predicate, the variable x is called

Answer 16

Argument

Question 17

Another method of changing propositional function into proposition. may be universal or existential

Answer 17

Quantification

Question 18

Universal quantification define__

Answer 18

“P(x) is true for all values of x in the domain of discourse”

Question 19

What does the domain of Discourse specify?

Answer 19

specifies the possible value of X

Question 20

” There exist an element in x in the domain of discourse such that P(x) is true”

Answer 20

Existential Quantification

Question 21

What are the Methods of Proof?

Answer 21

Direct Proof, Indirect proof, Proof by contradiction, and Existence Proof.

Question 22

A proof that p implies q is true by showing that q is true, if p is true

Answer 22

Direct proof

Question 23

A proof that p implies q is true by showing that p must be false, if q is false.

Answer 23

Indirect proof

Question 24

A proof that the proposition p is true based on the truth of ~p implies q, where q is a contradiction.

Answer 24

Proof by Contradiction

Question 25

A proof of the proposition of the form ∃x: P(x)

Answer 25

Existence Proof

Question 26

Classification of Existence Proof____

Answer 26

Constructive Existence Proof and Non-Constructive Existence Proof

Question 27

Establishes the assertion by exhibiting a value c such that P(c) is true.

Answer 27

Constructive Existence Proof

Question 28

The ¬ operator has higher precedence than

Answer 28

∧/ conjunction/ and

Question 29

∧ has higher precedence than

Answer 29

∨/ disjunction/ or

Question 30

∨ has higher precedence than

Answer 30

⇒/ implication/ conditional/ if and then

Question 31

⇒ has higher precedence than

Answer 31

⇔/ biconditional/ if and only if

Question 32

(p ∧ q), is true if both p and q are true, and is false if either p is false or q is false or both are false.

Answer 32

Conjunction

Question 33

(p ∨ q) is true if either p is true or q is true, or both p and q are true, and is false only if both p and q are false.

Answer 33

Disjunction

Question 34

(p ⇒ q) is false if p is true and q is false, and is true if either p is false or q is true (or both).

Answer 34

Implication or Conditional

Question 35

(p ⇔ q) is regarded as true if p and q are either both true or both false, and is regarded as false if they have different truth-values.

Answer 35

Biconditional

Question 36

called logical truths or truths of logic

Answer 36

Tautologies

Question 37

statements that come out as false regardless of the truth-values of the simple statements

Answer 37

Contradiction

Question 38

true for some truth-value assignments to its statement letters and false for others.

Answer 38

Contingent

Question 39

neither contradictory nor tautological

Answer 39

Contingent

Question 40

statements are said to be __________ if and only if all possible truth-value assignments to the statement letters making them up result in the same resulting truth-values for the whole statements.

Answer 40

logically equivalent

Question 41

An argument is ____________ if and only if its conclusion is a logical consequence of its premises.

Answer 41

logically valid