Deck 11: Rules of Inference and Quantifiers

Question 1

The rule of Hypothetical Syllogism ( H.S) is symbolized as

A)P ? q
B)P ? q.
C)P ? q,
D)P ? q..

Answer 1

P ? q.

Question 2

The rule of Absorption (Abs) is symbolized as

A)p.q
B)P ? q
C)p.
D)p

Answer 2

P ? q

Question 3

The rule of Simplification (Simp) is symbolized as

A)P ? q
B)P . q
C)P
D)p

Answer 3

P . q

Question 4

The rule of Addition is symbolized as

A)p
B)p.
C)P
D)p . q

Question 5

The rule of Conjunction (Conj) is symbolized as

A)p . q
B)p
C)p.
D)P

Question 6

Name the rule of inference P . Q) ? P V Q)

A)Commutation ( Com )-
B)Association (Assoc )-
C)De Morgan's Theorem De M )
D)Distribution Dist )

Question 7

Name the rule of inference p v q ) ? q v p )

A)Commutation ( Com )-
B)De Morgan's Theorem De M )
C)Distribution (Dist )
D)Association (Assoc )-

Question 8

Name the rule of inference [ p v q v r ) ] ? [ p v q ) v r ]

A)De Morgan's Theorem De M )
B)Distribution Dist )
C)Association (Assoc )-
D)Commutation ( Com )-

Question 9

Name the rule of inference [ p . q v r ) ] ? [ p . q ) v p. r) ]

A)Association (Assoc )-
B)Distribution (Dist )
C)De Morgan's Theorem De M )
D)Commutation Com )

Question 10

Name the rule of inference P ? p

A)Transposition (Trans )-
B)Material Implication (Impl)-
C)Double Negation ( D .N )-
D)Tautology ( Taut )-

Question 11

Name the rule of inference ( P ? q ) ? Q ? P )

A)Double Negation ( D .N )-
B)Tautology ( Taut )-
C)Transposition (Trans )-
D)Material Equivalence ( Equiv )-

Question 12

Name the rule of inference ( P ? q ) ? P v q )

A)Material Implication (Impl)-
B)Transposition (Trans )-
C)Material Equivalence ( Equiv )-
D)Exportation ( E x p)-

Question 13

Name the rule of inference P ? q ) ? [ p ? q ) . ( q ? p ) ]

A)Material Implication (Impl)-
B)Transposition (Trans )-
C)Tautology
D)Material Equivalence ( Equiv )-

Question 14

Name the rule of inference [ (P . Q ) ? r ) ] ? [ p ? ( q ? r ) ]

A)Transposition (Trans )-
B)Material Equivalence ( Equiv )-
C)Material Implication (Impl)-
D)Exportation ( E x p)-

Question 15

Name the rule of inference P V Q) ? P . Q )

A)Material Implication (Impl)-
B)De Morgan's Theorems De M )
C)Exportation ( E x p)-
D)Distribution (Dist )

Question 16

Name the rule of inference p . q ) ? q . p )

A)Commutation ( Com )-
B)Distribution (Dist )
C)Exportation ( E x p)-
D)Transposition (Trans )-

Question 17

Name the rule of inference [ p . q . r ) ] ? [ p . q ) . r ]

A)Exportation ( E x p)-
B)De Morgan's Theorems De M )
C)Association (Assoc )-
D)Distribution (Dist )

Question 18

Name the rule of inference P ? q ) ? [ p . q ) v P . Q ) ]

A)Exportation ( E x p)-
B)Material Equivalence ( Equiv )-
C)Distribution (Dist )
D)Material Implication (Impl)-

Question 19

Name the rule of inference p ? p . p )

A)Material Implication (Impl)-
B)Commutation ( Com )-
C)Tautology ( Taut )-
D)Association (Assoc )-

Question 20

The process of obtaining a proposition from a propositional function by substituting a constant for a variable is called …………………………………

A)quantification
B)deduction
C)instantiation
D)generalization

Question 21

General propositions can be regarded as resulting from propositional functions by a process called

A)instantiation
B)substitution
C)deduction
D)quantification

Question 22

The phrase 'Given any x' is called …………………………………….

A)a propositional function
B)a universal quantifier
C)truth-function
D)an existential quantifier

Question 23

Universal quantifier is symbolized as …………

A)' x)'
B)? ?x)'
C)' X'
D)' ?x'

Question 24

The phrase ' there is at least one x such that' is called ………………………………

A)a universal quantifier
B)a propositional function
C)an existential quantifier
D)truth-function

Question 25

An 'existential quantifier' is symbolized as ,

A)' ?x'
B)' x)'
C)' X'
D)( ?x )