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## Selasa, 24 Januari 2012

### SETS OPERATION

There are four operations on set, they are:
a. Sets intersection
b. Sets Union
c. Difference of a set
d. Complement of a set
We are going to discuss each other.
A. Sets Intersection
The intersection of sets A and B, written as A$\dpi{50} \bigcap$B, is a set of elements which are common to A and B, that is, those elements which belong to A and which belong to B.
A$\dpi{50} \bigcap$B= { x|x $\in$A and x $\in$B}.
Example:
Determine the intersection of A = {factor of 50} and B ={five first prime numbers}. Then determine n(A$\dpi{50} \bigcap$B).
Solution:
A = {1,2,5,10,25,50}
B = {2,3,5,7,11}
The elements common to A and B are 2 and 5. Thus, A$\dpi{50} \bigcap$B ={2,5}.
Because there are two elements in set A$\dpi{50} \bigcap$B, then n(A$\dpi{50} \bigcap$B)=2.
B. Union
The union of two sets A and B is denoted by A$\dpi{110} \cup$B. The union of two sets A and B is the set of all elements which belong to A or to B or to both. The union of A and B is denoted by
A$\dpi{50} \cup$B = {x|x $\in$A or x $\in$B}.
Example:
Find A$\dpi{110} \cup$B if A = {a,b,c,d} and B = {d,e,f,g}.
Solutions:
The elements of the union of set A and B are a,b,c,d,e,f and g.
Thus, A$\dpi{110} \cup$B ={a,b,c,d,e,f,g}.
C.Difference of Sets
The difference of sets P and Q, written as P-Q, is the set of elements which belong to P but which do not belong to Q.
P-Q={x|x $\in$P and X $\notin$Q}.
Example:
Let:
P = {a,b,c,d,e}
Q = {c, d, e, f,g h}
Determine:
a. P-Q
b. Q-P
Solution:
a. P-Q={a,b,c,d,e}-{c,d,e,f,g,h}
={a,b}
b.Q-P = {c,d,e,f,g,h}-{a,b,c,d,e}
={f,g,h}
d. Complement of a Set
The complement of a set A, denoted by $\bar{}$ is the set of elements which do not belong to A.
$\bar{}$= {x|x$\notin$A}.
Example:
Given universal set S = {1,2,3,4,5,6,7,8}
let A={prime numbers}
B = {1,2,3,4,5}.
Determine:
a. Complement of A.
b. Complement of B.
c. Complement of (A$\dpi{110} \cap$B).
Solution:
a. Complement of A = { 1,4,6,8}
b. Complement of B = {6,7,8}
c. Complement of (A$\dpi{110} \cap$B)= {1,4,6,7,8}.