Outline of COT 3100 material for first exam
I. Logic
A. Symbols(
∧
,
∨
, and
¬
)
B. Truth Tables
C. Logic Laws
D. Methods of showing equality of logical expressions
E. Implication Rules
F. Contrapositive of a stmt.
G. Quantifiers
II. Sets
A. Symbols(
∩
,
∪
,
∈
,
∅
,
¬
,
∉
, and
⊂
)
B. Set Laws
C. Membership Table
D. Proof Techniques for ifthen statements
i. direct proof
ii. proof of contrapositive
iii. proof by contradiction
E. How to Disprove an ifthen statement
F. InclusionExclusion Principle
Reading in texbook: 2.1 – 2.5, 3.1 – 3.3
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1) In a language survey of students it is found that 80 students
know English, 60 know French, 50 know German, 30 know
English and French, 20 know French and German, 15 know
English and German and 10 students know all three languages.
How many students know
a) at least one language?
b) English only?
c) French and one but not both out of English and German?
d) at least two languages?
Use the inclusionexclusion principle to handle each of these
questions.

A
∪
B
∪
C = A + B
+
C
–

A
∩
B

–

B
∩
C

–

A
∩
C

+ 
A
∩
B
∩
C
.
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 Spring '09
 Logic, Intersection, Mathematical proof, A ∩ B

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