2. SECTION SUMMARY
Set operations
Union
Intersection
Complementation
Difference
More on set cardinality
Set identities
Proving identities
Membership tables
3. UNION
DEFINITION:
Let A and B be sets.the union of the sets A and B
,denoted by AUB,is the set:
Example:what is{1,2,3} U {3,4,5}?
Solution:{1,2,3,4,5}
{X|XE A V XE B}
U
A B
4. INTERSECTION
Definition:The intersection of sets A and B,denoted by
AnB,is
Then A and B are said to be disjoint
Example:what is {123}n {345}
Solution:[3]
{X|X E A ^ X E B
U
A B
5. COMPLEMENTED
Definition:If A is set,then the complement of the A
denoted by A is the set U-A
Example:if U is the positive integers less than 100,what is
the complement of{x |x>70}
A={X E U| X E|A
A
AA
6. DIFFERENCE
Definition:Let A and B be sets.the difference ofA and B
,denoted by A-B,is the set containing the elements of A
that are not inB,
The difference of A and B is called complement of B with
respect to A.
Venn diagram A-B
A-B={X|X E A^ X E B}=AnB
COMPLEMENT
A B
U
7. CARDINATY OF THE UNION
OF TWO SETS
EXAMPLE:
Let A be the math majors in your class and B be the
CS majors.
To count the number of students who are either math
major or CS major,add the number of math majors and the
numbers of CS majors,and subtract the number of joints
CSmath majors.
9. SYMMETRIC DIFFERENCE
Definition:The symmetric difference of AandB
denoted by AOB is the set
(A-B)U(B-A)
EXAMPLE:
U={0,1,2,3,4,5,6,7,8,9,10}
A={1,2,3,4,5} B={4,5,6,7,8}
SOLUTION:
{1,2,3,6,7,8}
A B
dffierenced
10. VENN DIAGRAM WITH 3 SETS
A
AUB
BnC
C”
AnBnC
2 3 1 8
5 C
A B
C
U
9
11. SET IDENTITES
IDENTITY LAWS
A U =A AnU=A
Domination laws
AuU=U An=0
Idempotent laws
AUA=A AnA=A
Complementation law
(A)=A
13. PROVING SET IDENTITES
Different ways to prove set identites:
Prove that each set is a subset of the other.
Use set builder notation and propositional logic.
membership tables:verify that elements in the same
combination of sets always either belong or do not belong
to the same side of the identity.
Use 1 to indicate it is the set and a 0 to indicate that it is
not.
14. CONCLUSION
Restored sets of values in a dynamic databases are simply
read and write operations with respect to the databases
respectively.although the values used during restortation
are typically two operations reading and writing.