TOPIC: SETS
- Idea of a set, set notations and applications.
- Disjoint sets , Venn diagram
A. IDEA OF SET, NOTATIONS, APPLICATIONS.
Definitions:
A set can be defined as a group or a collection of well defined objects or numbers e.g collection of books, cooking utensils.
A set is denoted by capital letters such as P, Q, and R e.t.c while small letters are used to denote the elements e.g. a, b, c
Elements of a set: These are the elements or members of a given set. The elements are separated by commas and enclosed by a curly bracket {}
e.g M ={ 1, 3 ,5, 7, 11}, 1 is an element of M.
Example: Write down the elements in each of the following sets.
A = {Odd numbers from 1 to 21}
F = {factors of 30}
M = {Multiples of 4 up to 40}
Solution:
A = { 1,3,5,7,9,11,13,15,17,19,21}
F = {1, 3, 5, 6, 10, 15, 30}
M = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}
Set Theory
Weekend Assignment
1. Given that µ= {-10≤ x ≤ 10}, p= { -10 < x< 10}, Q= { -5 < x ≤ 3}. Which of the following is correct? I PI n Q II P U Q =µ III PI C QI
A. I and II only B. I and III only C II and III only
2. P and Q are subsets of the µ={x is an integer and 1< x < 15}, P= { x is odd} and Q= { x is prime}, find n(PI n QI) A. 3 B. 4 C. 5
Use the information below to answer question 3 and 4, µ= {1, 2, 3… 10}, A= {2, 4, 6, 8, 10} B= {1, 3, 9} and C = {2, 5, 7}
3. AI n C is A.{5, 7} B. { 1, 3, 4} C. { 6,7,8,9}
4. BI U C A.{2,4,5,7,8,10} B.{2,4,5,6,7,8,10} C.{ 1, 2,3,4,5, 9}
5. A set contains 7 members; find the number of subsets that can be obtained from it. A. 32 B. 64 C. 128
Theory
1. During one year in a school, 5/8 of the students had measles, ½ had chickenpox and 1/8 had neither. What fraction of the school had both measles and chickenpox?
2. In a class of 50 pupils, 24 like oranges, 23 like apple and 7 like the two fruits.
- How many do not like oranges and apples (b) What percentage of the class like apples only
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