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SET THEORY
I. State if the following are sets or not
a. All red dresses in a shop – Yes, it is a set ( as it is defined clearly)
b. All costly dresses in a shop – No, it is not a set ( as costly can mean any amount and it is
not defined clearly)
c. All ruled books in a shelf - Yes, it is a set
d. All soft linen in a shop – No ,it is not a set since soft linen is not defined clearly
e. All phones in an electronic shop - Yes, it is a set
II. Write true or false and correct the statement for the ones which are false
a. E belongs to a set of vowels - True
b. Carrot belongs to the set of vegetables - True
c. History belongs to the set of science subjects - False
Corrected Statement: History belongs to the set of social studies subjects
d. Amoeba belongs to the set of multicellular organisms - False
Corrected Statement: Amoeba belongs to the set of unicellular organisms
e. Stars belong to the galaxy - True
f. May does not belong to the months in a year – False
Corrected Statement: May belongs to the months in a year
g. In a set , elements are repeated – False
Corrected Statement: In a set elements are never repeated
III. Insert the right symbols
a. Scissors Є class of levers
b. Yellow spot Є part of the brain
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c. Blue pens Є set of stationery
d. Black Є colors in the rainbow
IV. Write is set language
a. 2 does not belong to the set of odd numbers
2 Є { set of odd numbers}
b. 15 belongs to the set of number divisible by 5
15 Є { set of numbers divisible by 5}
c. 20 belongs to set of first five numbers divisible by 10
20 Є { 2, 5, 10, 15, 20}
d. 2.3 does not belong to the set of fractions
2.3 Є { set of fractions}
e. Jasmine does not belong to the set of the vegetables
Jasmine Є { set of vegetables}
f. Mars belongs to the set of planets
Mars Є { Set of planets}
g. 7 belongs to the set of all prime numbers
7 Є { Set of all primes}
V. Fill in the blanks
a. The other name for set builder form is Rule Method
b. A set is a collection of well defined objects
c. In Roster form the elements are listed in brackets and separated by comma
d. The other name of Roster form is Tabular Form
e. In Set builder form the set is in the form of a statement
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f. Objects of a set are called elements or numbers
g. A = { 5, 10,5,20} is Roster form or Tabular Form
h. N= {x | x is a natural number} is in Rule or Set builder form
i.
In set theory, Є stands for Epsilon
VI. Express the following in Roster form
a. All planets in the solar system
A= { Mercury, Venus, Earth , Mars, Jupiter, Saturn, Neptune, Pluto}
b. All vowels in English alphabet
V = { a, e, i, o, u}
c. All letters in the word Mathematics
L = { M, A, T, H, E,I, C,S} ( The letters that are repeated are written only once as
elements are never repeated in sets)
d. All months that have 31 days
M = { January, March, May, July, August , October, December}
e. All odd number lesser than 10
O = { 3, 5, 7, 9}
VII. Express the following in Set Builder form
a. The set of integers
I = { x | x belongs to the set of integers}
b. S = { 40,42,44,46,48,50}
V = { x | x is a prime number between 40 and 50}
c. N = { 27,29,30,33,36}
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P = { x | x is a multiple of 3 between 27 and 36 }
d. All days of the week
W = { x | x belongs to all days of the week}
e. All consonants of the English alphabet
C = { x | x belongs to the set of all consonants of the English alphabet}
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SUMMARY – BASICS OF SET THEORY
Basics
A Set is a well defined collection of objects
Objects that make up a set are called Elements or numbers
o Example of a set A = { 1,2,3,4,5}
o 1, 2,3,4 and 5 are the elements of the set
Elements in a set are never repeated
Member and not a member
o 3 Є { 1,2,3,4} (belongs)
But
o 3 Є { 2,4,6,8}( does not belong)
Representation of sets
Roster Method/Tabular Method – Elements are listed in brackets with commas
o Example N = { 3,5,7,9}
Set Builder/Rule form – It is in the form of a statement
o Example N = { x| x is the first 4 odd numbers}
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