in the If they were unsure of the address, then they would have telephoned. ers
ID: 3878102 • Letter: I
Question
in the If they were unsure of the address, then they would have telephoned. ers a .:. They were sure of the address. Use truth tables to determine whether the argument forms in 6- 11 are valid. Indicate which columns represent the premises and which represent the conclusion, and include a sentence explain- ing how the truth table supports your answer. Your explanation should show that you understand what it means for a form of argument to be valid or invalid. d b umber, 6. 7. P nterior 3600 . ~q pExplanation / Answer
6 p->q
q->p
Conclusion p v q
So basically we are having:
(p->q) (p->q) ---> p v q
So we need to create two truth tables(one for the premises and one for the conclusion)
and comapre their results and if they are same the conclusion holds otherwise it does
not hold.
Showing both the truth tables together we get:
C3,C4 and C5 shows the premises
C6 shows the comclusion
C1 C2 C3 C4 C5 C6
p q p->q q->p (p->q) (p->q) p v q
F F T T T F
T F F F F T
T T T T T T
T F F F F T
As columns C5 and C6 are not matching, so the conclusion does not hold true for the given premises
7 p
p->q
~q v r
Conclusion r
So basically we are having:
((p) (p->q)(~q v r)) --> r
So we need to create two truth tables and comapre their results and if they are same the
conclusion holds otherwise it does not hold.
Showing both the truth tables together we get:
C1,C4,C5,C6 shows the premises
C3 shows the conclusion
C1 C2 C3 C4 C5 C6
p q r p->q ~q v r (p (p->q)(~q v r)
F F F T T F
F F T T T F
F T F F F F
F T T F T F
T F F F T F
T F T F T F
T T F T F F
T T T T T T
C3 and C6 are not matching so it does not hold
8 p v q
p->~q
p -> r
Conclusion r
So basically we are having:
((p v q) (p->~q)(p -> r)) --> r
So we need to create two truth tables and comapre their results and if they are same the
conclusion holds otherwise it does not hold.
Showing both the truth tables together we get:
C4,C5,C6,C7 shows the premises
C3 shows the conclusion
C1 C2 C3 C4 C5 C6 C7
p q r p v q p->~q p->r ((p v q) (p->~q)(p -> r)
F F F F F T F
F F T F F F F
F T F T T T T
F T T T T F F
T F F T T F F
T F T T T T T
T T F T F F F
T T T T F T F
C3 and C7 are not matching so it does not hold
9 p ^ q -> ~r
p v ~q
~q -> p
Conclusion ~r
So basically we are having:
(( p ^ q -> ~r) (p v ~q)(~q -> p)) --> ~r
So we need to create two truth tables and comapre their results and if they are same the
conclusion holds otherwise it does not hold.
Showing both the truth tables together we get:
C4,C5,C6,C7 shows the premises
C3 shows the conclusion
C1 C2 C3 C4 C5 C6 C7
p q r p^q->~r pv~q ~q->p ((p^q->~r)(pv~q)(~q->p))
F F F F T F F
F F T T T F F
F T F F F T F
F T T T T T T
T F F F T T F
T F T T T T T
T T F T T F F
T T T F T F F
C3 and C7 are not matching so it does not hold
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