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Unformatted text preview: PHL 245  Test One — October 23. 2006
Name: Student #: t fry, .' . ._ i. Lt
‘ l Concepts 1: Indicate whether the following are true or false, and explain your answers brieﬂy. (6
marks) (1') A disjunction with one truthfunctionally true disjunct must itself be truthfunctionally true. True. The disjunct that is truthfunctionally true is true no matter what. Thus one of the disjuncts is
true no matter what. That true disjunct will make the entire disjunction true. Thus the full
disjunction is always true; it is itself truthfunctionally true. (2) if an argument has true premises and a true conclusion, we know it is a perfectly good argument. False. An argument with true premises and a true conclusion needn't be either valid or sound.
That is because the truth of the premises and the conclusion does not guarantee that the conclusion
follows from the premises (or that it is impossible for the premises to be true and the conclusion false).
Thus it needn't be valid. And validity is an essential component of soundness. (3) Any argument that includes among its premises "Noone is a Jedi Knight" and “Salacious Crumb is
a Jedi Knight” is deductiver valid. True. These two premises are inconsistent. Thus, any statement follows from them. {it is
impossible for all the premises to be true and this other statement false. since the premises
can't all be true.) So, no matter what the conclusion ofthe argument is. it follows from the
premises. and the argument is valid. Concepts [1: For each of the following, either give an example or explain why it is impossible to do so.
(4 marks) (1) A pair of sentences that are logically equivalent and both false.
Radiohead recorded Sgt. Pepper.
Sgt. Pepper was recorded by Radiohead. (2) A consistent set of sentences, all of whose members are false.
{ The sky is green. Grass is blue. } /
/ / Symbolizations: Symbolize the following using the interpretations given. (10 marks) I A: Anakin is a Sith Lord } B: Ben Kenobi is Sith Lord
C: Chewbacca is a Sith Lord.
D: Anakin built a droid.
12': Ben Kenobi likes Ewoks.
F: The Force is in balance. ( 1) Exactly one of Anakin, Ben Kenobi. and Cliewbacea is a Sith Lord. 1A&(~B&~C)]v[[B&(~A&~C)lv[C&(—~A&~B)H (2) If the Force is in balance. then Ben Kenobi is a Sith Lord if and only if neither Anakin nor
C hewbacca is. F3[BE(~A&~C)] (3) Anakin is a Sith Lord unles the Force is in balance, in which case he isn‘t but Ben Kenobi and
Chewbacca are. (A&~F)V[F&(~A&(B&C))] (4) If any of them is a Sith Lord, then so are the other two. (Av(BvC))3(A&(B&C)) (5) Chewbacca is a Sith Lord. if and only if, Anakin built a droid only if Ben Kenobi likes Ewoks. CE(D:>E) TruthTables: (1) Construct a ﬁll! truth—table to determine whether the following is a mothfunctional truth, a truth— functional falsehood, or a truthfunctionally indeterminate sentence (make sure you indicate
which it is). (10 marks) ~(C&B):>[AV(BEC)]

/3‘ L m q “ T.
r v T‘ m ‘ L1 F T I a "17" {I T' 'F' g \j (2) Show the following set of sentences is truthfunctionally consistent. using a shortened truthtable.
(5 marks). {FD(JVK),FE~J} 7 r T T T ‘3. "l Why is it necessary to construct ajiiﬂ truthtable to show that a set of sentences is truthﬁmctionaﬂy
inconsistent, while it is only necessary to construct a shortened truthtable to show that such a set is
truthfﬁmctionaﬂy consistent? (5 marks) Proving inconsistency means proving that it is impossibie for all members of the set to be true
on a single truthvalue assignment. Thus we must list every such assignment, to make sure none allow
this possibility. Proving consistency, on the other hand, only means proving it is possible for all members of the
set to be true on a single truthvalue assignment. Thus we must only ﬁnd a single assignment (one on
which this possibility is actualized). Mation in SD. (10 marks)
Given the assumptions: AE~(BE~C)
~(AVB) Derive: C Asa (fail—H]
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