Exam 1 Material

Question 1

What is a tautology?

Answer 1

A formula that outputs true on every truth-assignment (input).

Question 2

What is a contradictory?

Answer 2

A formula that outputs false on every truth assignment (input).

Question 3

What is a contingent formula?

Answer 3

A formula that outputs true for some truth assignments (inputs) and false for others.

Question 4

A satisfiable formula (sat) is…

Answer 4

A formula for which there exists a truth-assignment that makes the formula’s output true.

Question 5

p -> q is a “guarded” or “triggered” two-step proposition because…

Answer 5

We only concern ourselves about q (second step) if the guard/trigger, p (first step) is true.

Question 6

The precedence order for the 4 basic logical connectives is (from highest to lowest):

Answer 6

~ (NOT)
^ (AND)
v (OR)
–> (IMPLIES)

Question 7

The associativity of the AND (^) connector means that its always combines to the…

Answer 7

Left

Question 8

The associativity of the OR( (v) connector means that it always combines to the…

Answer 8

Left

Question 9

The associativity of the IMPLIES (–>) connector means that it always combines to the…

Answer 9

Right

Question 10

Linear temporal logic:

Answer 10

Supports reasoning about event sequencing

Question 11

Propositional logic:

Answer 11

Supports reasoning about propositions (statements that are true or false) and about valid ways of drawing conclusions from premises

Question 12

A (valid) argument consists of sentences (claims) chained together in such a way that the truth of each sentence…

Answer 12

1. Is assumed (i.e., the sentence is a premise) or…

2. Follows from the truth of the previous sentences (via inference or deduction).

Question 13

In a valid argument, if all of the premises are true, then…

Answer 13

…the conclusions must be true.

Question 14

Act of inference:

Answer 14

Attempting to establish the truth of the conclusions from the truth of the premise.

Question 15

Valid inference:

Answer 15

The “transmission of truth” such that in every situation where all the premises P are true, the conclusion Q is also true.

Question 16

Syllogism:

Answer 16

Consists of exactly 2 premises and a conclusion, whose validity is determined by the underlying structure of the argument.

Question 17

Negation (~) can be recognized in an English sentence by…

Answer 17

the presence of the word “not” or morphemes like “un-“ or “ir-“.

Question 18

Conjunction (^) can be recognized in an English sentence by…

Answer 18

the presence of the words “and” or “both”.

Question 19

An exclusive OR (disjunction)…

Answer 19

Capture two events that cannot occur simultaneously (either/or). Can be represented as (p V q) ^ ~(p ^ q)

Question 20

An inclusive OR (disjunction)…

Answer 20

Captures two events that can occur simultaneously or alone (either… or both).

Question 21

Implication (–>) is used to capture…

Answer 21

Conditionality.

Question 22

Implication (–>) can be recognized in an English sentence by words such as…

Answer 22

If…then...,
… provided that,
 assuming,
 only if...,
 given…

Question 23

A fact C is said to be “known” by person P if…

Answer 23

• C is true, and…
  
  • P believes C to be true, and…
    
    • P has some sort of justification that C is true (C is not something that P arrived at by a guess or chance.)

Question 24

Deduction:

Answer 24

The synthesis of new facts (consequences) from known facts via truth-preserving inferences.

Question 25

^i

AND Introduction Rule

Answer 25

Provided that there are proofs for P and Q, then one can conclude that P^Q is true.

^i :      P Q
     ------------
    P ^ Q

Question 26

^e1

AND Elimination Rule 1

Answer 26

A rule to eliminate the RIGHT operand Q, leaving P:

^e1 : P ^ Q
——–
P

Question 27

^e2

AND Elimination Rule 2

Answer 27

A rule to eliminate the LEFT operand P, leaving Q:

^e2: P ^ Q
——–
Q