Uploaded by Ampuan Norhaslinda A Hj Said

# Sets ```CHAPTER 2 : SET LANGUAGE AND NOTATION

A set is well-defined collection of items where each item is called an element. A set is defined by
 listing the elements of the set e.g. {1, 2, 3, 4, 5, 6}
 using a variable and a sentence e.g. {x : x is an integer and 0 &lt; x &lt; 7}

A finite set is a set with a finite number of elements.

An infinite set is a set with an infinite number of elements.

An empty set or null set,  or { } , is a set with no elements.

Two sets are said to be equal if they have exactly the same elements.

A set S is a subset of set P, i.e. S  P, if every element of S is an element of P.

A set Q is a proper subset of P, i.e. Q  P, if every element of Q is an element of P but there is at
least one element of P that is not an element of Q.

The universal set, ξ , is a set containing all elements being considerd in a discussion.

The complement of a set A, denoted as A which consists of all elements in the universal set that
are not in A.

Venn diagrams are used to illustrate the relationship between sets.

For any set A, the number of elements in A plus the number of elements in A equals the number
of elements in ξ . That is, n (A) + n ( A ) = n (ξ )

The union of sets P and Q, denoted as P  Q , is the set of all elements that are in P or in Q or in
both P and Q.

The intersection of sets P and Q, denoted as P  Q, is the set of all elements that are common to
P and Q.

Two sets, P and Q, are said to be disjoint sets if they do not have any common elements.
That is, P  Q, = 
Example :
ξ = {x : x is an integer, 1  x  14 }
P = { x : x  6}
Q = {x : x is even }
R = { x : x is a two-digit number}
(a) On the given Venn diagram insert the members of the sets in the appropriate regions.
(b) List the members of Q  ( P  R )
(c) Find
(i)
n ( P  R )
(ii)
n ( P  Q )
Solution :
(a)
ξ
P
Q
R
Example:
(a) For each of the following where ξ = A  B  C, use the Venn diagram to represent the given sets
(i) (A  B )  C
(ii) (B  C )  A
(b) For each of the following where ξ = A  B  C, define, in terms of one or more of A, B and C,
the set indicated by the shaded region (s)
(i)
(ii)
(c) It is given that
ξ is the set of polygons,
T is the set of triangles,
P is the set of parallelograms,
R is the set of rhombuses and
S is the set of squares.
Draw a clearly labelled diagram to show relationship between these sets.
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