Quiz 5

Question 1

Generalized De Morgan’s Laws

Answer 1

¬(∀xP(x)) ≡ ∃x¬(P(x))

Question 2

Generalized De Morgan’s Laws

Answer 2

¬(∃xP(x)) ≡ ∀x¬(P(x))

Question 3

Exactly One…

Answer 3

∃x(1?(x) ∧ 2?(x) ∧ ∀y[(1?(y) ∧ 2?(y)) → (y = x)] x, y ∈ ?

Question 4

Exactly Two…

Answer 4

∃x∃y(1?(x) ∧ 1?(y) ∧ (x≠y) ∧ ∀z[1?(z) → (x = y ∨ z = y)] x, y, z ∈ ?

Question 5

Argument

Answer 5

A connected series of statements to establish a definite proposition.

Question 6

Inductive Argument

Answer 6

An argument that moves from specific observations to general conclusions.

Question 7

Deductive Argument

Answer 7

An argument that uses accepted general principles to explain specific situations.

Question 8

Valid Argument

Answer 8

Any deductive argument in the form of (p1, p2, p3…, pn) → is _____ if the conclusion follows from those hypotheses.

Question 9

Sound Argument

Answer 9

A valid argument that also has a true hypothesis.

Question 10

Rule of Inference: Addition

Answer 10

p /∴ p ∨ q

Question 11

Rule of Inference: Simplification

Answer 11

p ∧ q /∴ p

Question 12

Rule of Inference: Conjunction

Answer 12

p, q /∴ p ∧ q

Question 13

Rule of Inference: Modus Ponens (“Method of Affirming”)

Answer 13

p, p → q /∴ q

Question 14

Rule of Inference: Modus Tollens (“Method of Denying”)

Answer 14

¬q, q → p /∴ ¬p

Question 15

Rule of Inference: Hypothetical Syllogism (“Transitivity of Implication”)

Answer 15

p → q, q → r /∴ p → r

Question 16

Rule of Inference: Disjunctive Syllogism

Answer 16

p ∨ q, ¬q /∴ p

Question 17

Rule of Inference: Resolution

Answer 17

p ∨ q, ¬p ∨ r /∴ q ∨ r

Question 18

Synonym: “Syllogism”

Answer 18

Deduction

Question 19

Universal Instantiation

Answer 19

∀xP(x), x ∈ D /∴ P(d) if d ∈ D

Question 20

Universal Generalization

Answer 20

P(d) for any d ∈ D /∴ ∀xP(x), x ∈ D

Question 21

Existential Instantiation

Answer 21

∃xP(x), x ∈ D /∴ P(d) for some d ∈ D

Question 22

Existential Generalization

Answer 22

P(d) for some d ∈ D /∴ ∃xP(x), x ∈ D

Question 23

Fallacy

Answer 23

An argument constructed with an improper inference.

Question 24

Fallacy: Affirming the Consequent

Answer 24

If Juan is in Dallas, than he is in Texas. He is in Texas. Therefore, he is in Dallas.

Question 25

Fallacy: Denying the Hypothesis

Answer 25

If Ingrid is in Dallas, she is in Texas. She isn't in Dallas. Therefore, she is not in Texas.

Question 26

Fallacy: Begging the Question

Answer 26

I'm not lying so I must be telling the truth.

Question 27

Fallacy: Interrogation

Answer 27

Have you stopped annoying your spouse?

Question 28

Fallacy: No True Scotsman

Answer 28

No true American opposes tax cuts.

Question 29

Specious Reasoning

Answer 29

An unsupported or improperly constructed argument. (That is, an unsound or invalid argument.)

Question 30

Conjecture

Answer 30

A statement with an unknown truth value.

Question 31

Theorem

Answer 31

A conjecture that has been shown to be true.

Question 32

Proof

Answer 32

A sound argument that establishes the truth of a theorem.

Question 33

Lemma

Answer 33

A simple theorem whose truth is used to construct more complex theorems.

Question 34

Corollary

Answer 34

A theorem whose truth follows directly from another theorem.