MATH1
Logic
Set theory
MATH1
Untis schedule
name
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Mrs. Agnes Veugen
Mr. Stan Hartingsveldt
Mr. Paul Linnartz
Mr. Andre Postma
Mrs. Suzana Andova
Mrs. Ella van der Sanden
Mr. Joris Geurts
Materials for Math1
Book:
Discrete ma
Week 3 propositions
Chapter 4, paragraph 4.8:
new logical operators
Switcheroo laws
1
Propositional laws (week 2)
F
2
Absorption laws (week 2)
The following laws also hold:
(11a) p (p q ) p
(11b) p (p q ) p
These are the Absorption laws
3
Exclusive
MATH2: Sets week 2
1.4 set operations
(without "Fundamental Product")
1.6 counting principles
5.2 more counting principles
1
Operations on sets
If we have 2 sets A and B, we can take
all the elements in A or in B
cfw_x | x A or x B
This is called u
MATH1 WEEK 4 EXERCISES
SETS
Exercise 4.1:
Prove: 1 + 4 + 7 + . + 3n2 = n (3n-1) / 2 for nN
Exercise 4.2:
Given the formally definition of sequence a, find a1, a2 , a6
a.
a0 = 3
an = an-1 + 2 for n 1
b.
a0 = 2
an = n*(an-1) for n 1
c.
a0 = 1
an = an-1 + n
MATH1 WEEK 3 EXERCISES
SETS
Exercise 3. 4:
Given A=[cfw_a,b,cfw_c,cfw_d,e,f].
a. List the elements of A
b. Find n(A)
c. Find the power set of A
Exercise 3. 2:
Let S=cfw_1,2,3.,8,9. Determine whether or not each of the following is a partition of S:
a. [cf
MATH1
Week 4
1
Week 4: Sets
1.8 Mathematical induction
3.5 Sequences
2
Week 4: Repetition
Sets of sets:
If S is a set, then the power set of S is
the collection of all subsets of S: P(S)
If S is a nonempty set, then a
partition of S is a subdivision of
MATH1 week 3: sets
1
Week 3 Sets
1.5 Algebra of Sets
(without "Duality")
1.7 Sets of sets
(without "Generalized Set Operations")
2
Algebra of sets
Note: similar to the propositional laws
3
Absorption laws
Again the extra laws:
A (A B) = A
A (A B) = A.
Week 4: Propositions
Chapter 4,
Paragraph 4.9 can be skipped.
Paragraph 4.10:
Quantifiers
ATTENTION: We use a different notation!
1
Repetition
operators :
exclusive OR
not mentioned in the book
laws :
absorption laws
not mentioned in the book
contraposit
MATH1 WEEK 2 EXERCISES
SETS
Exercise 2.1:
Show (by giving an example for A, B and C) that we can have:
A B = A C without B = C
Exercise 2.2:
Consider the universal set U=cfw_1,2,3,.8,9 and sets A=cfw_1,2,5,6, B=cfw_2,5,7,
C=cfw_1,3,5,7,9. Find:
a. A B
b.
MATH1 WEEK 1 EXERCISES
SETS
Exercise 1.1:
Which of these sets are equal?
cfw_x,y,z cfw_x,y,z,x cfw_y,x,y,z
cfw_y,z,x,y
Exercise 1.2:
List the elements of each set where N=cfw_1,2,3,.:
a. A =cfw_ x N | 3 < x <9
b. B =cfw_ x N | x is even, x < 11
c. C =cf
MATH1 Logic
week 2
1
week 2
Chapter 4, paragraph 4.6 and 4.7:
algebra of propositions
logical equivalence
laws
2
Logical equivalence
two propositions p and q are
(logically) equivalent
if they have identical truth tables.
denoted by
pq
3
Tautology/Cont
MATH1: Second lesson
Logic
Background material
Book: Discrete mathematics
(Seymour Lipschutz/Marc Lipson)
chapter 4:
Logic and Propositional calculus
Week 1: logic calculus
4.1 up to and including 4.5:
True or false
Proposition
a proposition is a sentenc