Review Of Basic Concept Of Set

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 P^I n Q    II P U Q =µ III P^I C Q^I

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(P^I n Q^I)   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.  A^I n C is  A.{5, 7}  B. { 1, 3, 4}   C. { 6,7,8,9}

4.  B^I 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.

1. How many do not like oranges and apples    (b) What percentage of the class like apples only