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Propositional Logic
Part A
Translate the following statements into symbolic form.
1.
2.
3.
4.
Passing the written exam is a necessary condition for getting a driving license.
Passing the written exam and the road exam is a necessary and sufficient condition for getting a
driving license.
If Tom gives me the money, then if Mary is willing to buy my laptop, then her buying my laptop
implies that I will have enough money left for the school fee.
5.
Earning a degree is a sufficient condition for making my parents happy only if the job market is
optimistic when I graduate.
Unless you cheat in the exam, you pass the exam provided that the exam is unfair.
6.
I eat neither pork nor beef.
Part B
Determine the truth values of the following compound proposition.
Suppose that A, B, C are true and X, Y, Z are false.
1. ((~X  Z)  (~C v B)) • ((~X • A)  (~Y • Z))
2. ~(~((C  ~B) • (Z  ~A)) • ~(~(B  Y) • (~X  Z)))
3. (Z  C)  (((~X  B)  (C  Y))  ((Z  X)  (~Y  Z)))
Part C
Use truth tables to determine whether the following propositions are tautology, self-contradiction, or
contingent proposition.
1. (S  R) • (S • ~R)
2. ((H  N) • (T  N))  ((H  T)  N)
3. ((F  E) • (G  H))  ((G • E)  (F • H))
Part D
Use truth table to determine whether the pairs of propositions are equivalent, contradictory, and
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consistent.
1. H  ~G
((G • H)  (~G • ~H))
2. M  (K  P)
(K • M)  P
3. R • (Q  S)
(S  R) • (Q  R)
Part E
Translate and determine whether the following argument is valid with a truth table.
If high school graduates are deficient in reading, they will not be able to compete in the modern world.
If high school graduates are deficient in writing, they will not be able to compete in the modern world.
Therefore, if high school graduates are deficient in reading, then they are deficient in writing.
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Part F
Use truth table to determine whether the following arguments are valid.
(1) ~(K  S)
S  ~(R v K)
R  ~S
(2) G  H
RG
~H  G
RH
Part G
Use indirect truth table to determine whether the following arguments are valid.
(1) P • (Q  R)
(P • R)  ~(S  T)
(~S  ~T)  ~(P • Q)
ST
(2) ~G  (~H • ~I)
JH
K  (L • M)
KJ
L•G
Part H
Use indirect truth table to determine whether the sets of propositions are consistent.
(1) (G  ~Q)  (F  B)
~(F  Q)
BN
(F  N)  Q
(2) G  P
P  (A • ~G)
(R  T)  G
YR
BT
YB