1
UNIVERSITY OF TECHNOLOGY, JAMAICA
SCHOOL OF MATHEMATICS & STATISTICS
COLLEGE MATHEMATICS 1A/B (MAT1044/1047)
TOPIC: SETS
WORKSHEET # 1
22

, 30 ,  , e, − 18,
1. Given the following set 1250, 49 ,
7

Identify those elements that belong to the set of:
(i) integers (ℤ)
(ii) rational numbers (ℚ)
2. State the number of elements in each set, if possible:
A =  x : x  , − 2  x  3
(i)
− 4, −
63 

7
(iii) irrational numbers (ℚ′)
(ii)
B = t : t  , t  9
(iv)
D =  y : y  , − 4  y  3
3. Express the following sets using interval notation:
(i)
Y =  x : x  , 5  x  9
(ii)
T =  x : x  , x  2 or x  4
4. Express the following intervals in set-builder notation:
(i)
(ii)
(iii)
(− 1, 9
− 7, + )
(− , − 8)
(iii)


C = x : x  , ( 2 x − 1) ( x 2 − 4 ) = 0
5. Let the universal set be the set of real numbers
7, 34)
A = (− 12, 7 and
(iv)
. A and B are intervals defined by
B = − 7, 12). Represent the intervals A and B on the real number line and find, using interval notation:
A'
A B
A− B
(i)
(ii) A  B
(iii)
(iv)
6. Let P and Q be intervals defined by P = − 4, 3) and Q = − 2, + ) . Using the number line, find:
P  Q , ( set builder notation)
(i)
(ii)
(P  Q)' , ( interval notation)
7. Represent the following intervals X = (− ,−1 and Y = (− 7, 0) on the real number line and express the
following in interval notation:
X Y
(i)
(ii)
( X Y )'
8. Let the universal set be the set of real numbers
. If sets A and B are (− 3, 4 and − 7, 8) respectively,
then use interval notation to represent the following:
A B
(i)
(ii)
A B
(iii)
(iv)
A' B
A'
B− A
(vi)
. Given the intervals M = (− , 0) and N = (− 12, 7,
express the following in both set builder and interval notation:
(i)
M N
(iv)
(M − N ) '
(ii)
(M  N ) '
A− B
(v)
9. Let the universal set be the set of real numbers
(iii)
(M  N ) '