Test 4 Study

Question 1

what is QE?

Answer 1

rule to swap quantifiers.
(∀x)¬(Px ∧ ¬Mx)
———————————-
¬(∃x)(Px ∧ ¬Mx) QE

Question 2

what is UI?

Answer 2

rule to remove universal quantifier
(∀x)(Rx –> Bx) can be replaced with (Rm –> Bm)

Question 3

what is EI?

Answer 3

rule to remove existential quantifier
(∃x)(Rx –> Bx) can be replaced with (Rm –> Bm)
has to be a new constant

Question 4

what is UG?

Answer 4

rule to introduce universal quantifier
(Wm –> Bm) to (x)(Wx –> Bx)

Question 5

what is EG?

Answer 5

rule to introduce existential quantifier
(∃x)

Question 6

fill in blank
¬(P ∧ Q)
_______________________
DeM

Answer 6

¬P ∨ ¬Q

Question 7

fill in blank
P –> Q
P
___________________________
MP

Answer 7

Q

Question 8

fill in blank
P –> Q
¬Q
____________________________
MT

Answer 8

¬P

Question 9

fill in blank
P –> Q
Q –> R
———————————
CA

Answer 9

P –> R

Question 10

fill in blank
P ∨ Q
¬P
——————————–
DA

Answer 10

Q

Question 11

fill in blank
P ∧ Q
———————————–
Simp

Answer 11

P

Question 12

fill in blank
P
Q
———————————
Conj

Answer 12

P ∧ Q

Question 13

fill in blank
P
———————————-
Add

Answer 13

P ∨ Q

Question 14

fill in blank
P –> Q
——————————
Imp

Answer 14

¬P ∨ Q

Question 15

fill in blank
P –> Q
——————————-
Contra

Answer 15

¬Q –> ¬P

Question 16

T / F : There are unbound variables in this expression: (Ab ∨ (Ba ∧ (∃x)Cx)

Answer 16

False

Question 17

T / F : This is a formula but not a WFF of PL: (∀x)(Rx → (∃x)Mx).

Answer 17

False. It’s not a formula.

Question 18

T / F : This is a correct application of the rule Conj: 7. (∀x)Rx ∧ (∃x)Mx Conj 5,6.

Answer 18

True

Question 19

T / F : This is a tautology: (∀x)(Bx → (Ax ∨ ¬Ax)).

Answer 19

True

Question 20

T / F : Any argument with contrary premises is valid.

Answer 20

True

Question 21

Which rule of PD adds an existential quantifier?

Answer 21

EG

Question 22

Apply QE to the following sentence. (∃x)¬(Px ∨ ¬Mx)

Answer 22

¬(∀x)(Px ∨ ¬Mx)

Question 23

Apply DeM to the following sentence. ¬(∀x)¬(Px ∨ ¬Mx)

Answer 23

¬(∀x)(¬Px ∧ Mx)

Question 24

Give proper rule abbreviations for 3 of the 5 new rules of PD.

Answer 24

QE, UI, UG, EI, EG

Question 25

What two sentences can you get from the following sentence using the rule Imp? (x)(Mx → Wx) ∨ (∃x)¬Mx

Answer 25

¬(x)(Mx → Wx) → (∃x)¬Mx (x)(¬Mx ∨ Wx) ∨ (∃x)¬Mx

Question 26

what's A/IP?

Answer 26

assumption for indirect proof, assumes the negation of the statement we want to prove

Question 27

what's A/CP?

Answer 27

assumption for conditional proof

Question 28

The universal quantifier represents a conjunction. The existential quantifier represents a what?

Answer 28

disjunction

Question 29

Which rule of PD removes a universal quantifier?

Answer 29

UI

Question 30

How many bound variables are there in the following WFF? (∀x)((Ax ∧ Bx) ∨ Ba)

Answer 30

1

Question 31

Give a sentence which is equivalent to the following and name the rule you used which connects them. ¬(∀x)(Rx → Bx)

Answer 31

(∃x)¬(Rx --> Bx), QE

Question 32

The disjunction of an I sentence and an O sentence is obviously a disjunction. But it is also a what (i.e. tautology, contradiction, contingent, large order of fries)?

Answer 32

contingent