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CA 208 Logic Ex1
In your own words, define the following

1.
2.
3.
Logic:
Valid reasoning/inference (2 equivalent definitions):
Propositions/statements:
List the

1.
2.
4 binary
1 unary
connectives (use the special symbols)
Translate the following into plain English

1.
2.
3.
4.
P |= C
{A,B} |= A  B
{A  B} |= A
{A, A → B} |= B
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CA 208 Logic Ex1
Formalise the following arguments/inferences using proposional
variables (P, Q, R, ...) and the logical connectives. State the
translation keys:

1.
2.
3.
4.
5.
Kate is a student. If Kate is a student, then Kate is broke. |= Kate is
broke.
Kate is a student. Kate is broke. |= Kate is a student and Kate is broke.
Kate is a student and Kate is broke. |= Kate is a student.
Kate is a student. |= Kate is a student.
Kate is taller than John. John is taller than Mike. If Kate is taller than
John and John is taller than Mike, then Kate is taller than Mike. |= Kate
is taller than Mike.
Intutively, are the inferences above logically valid (i.e. is the
conclusion true in all situations where the premises are true)?
Is the following inference logically valid?


1.
If Kate is a student, then Kate is broke. Kate is broke. (|= ??) Kate is a
student.
2
CA 208 Logic Ex1
Complete the following truth tables:
P Q PQ PQ
PQ
PQ
P
1
1
1
1
0
0
0
1
0
0
PQ  P  Q  P   Q ( P   Q)
P
P
Q
1
1
1
1
0
0
0
1
0
0
P P   P
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CA 208 Logic Ex2
What are






Tautologies
Contradictions
Contingencies
Define logical equivalence  in terms of 
Intuitively, what does it mean for two formulas
to be logically equivalent?
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CA 208 Logic Ex2
Use the truth table method to show whether
the following are tautologies, contingencies or
contradictions




(P  (P Q))  Q
(P  Q)  (PQ)
(Q  Q)
Use the truth table method and the definition of
logical equivalence in terms of the biconditional
(iff) to show that


(P  Q)  (P  Q)
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CA 208 Logic Ex2
Use the Boolean equivalences to show
(i.e.rewrite) that the following are logically
equivalent:



(Q  P)  (PQ)
(P  (Q  P))  (P  Q)
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