SET

SET

The collection of well-defined distinct objects is known as a set. The word well- 

defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not.

Generally the name of the set is given using capital letters A, B,C,.....

The members or elements of the set are shown by using small letters a, b, c...

Methods of writing sets

There are two methods of writing set.

(1)      Listing method or roster method

(2)       Rule method or set builder form

Practice set 1.1

Q1)  Write the following sets in roster form.

(i)           Set of even numbers

Ans. A = {2, 4, 6, 8 ...}

(ii)         (ii) Set of even prime numbers from 1 to 50

     Ans.  A = {2}

(iii)       Set of negative integers

Ans.  A = {-1, -2, -3 ...}

(iv)        Seven basic sounds of a sargam (sur)

      Ans.  S = {sa, re, ga, ma, pa, dha, ni}

Q2)  Write the following symbolic statements in words.

Answer

(i) 4/3  Is an element of set Q.

(ii) -2 is not an element of set N

(iii) Set P is a set of all p's such that p is an odd number.

Q3)  Write any two sets by listing method and by rule method.

Q4)  Write the following sets using listing method.

(i)           All months in the Indian solar year.

      Ans.  A = {Chaitra, Vaishakh, Jyeshth, Ashadh, Shravan, Bhadra, Ashwin, Kartik, Agrahayan, Paush, Magh, Phalgun}

(ii)         Letters in the word ‘COMPLEMENT’.

   Ans.  X = {C, O, M, P, L, E, N, T}

(iii)       Set of human sensory organs.

Ans. S = {Nose, Ears, Eyes, Tounge, Skin}

(iv)        Set of prime numbers from 1 to 20.

Ans. P = {2, 3, 5, 7, 11, 13, 17, 19}

(v)         Names of continents of the world.

Ans. C = {Asia, Africa, Europe, Australia, Antarctica, South America, North America} 

Q5) Write the following sets using rule method.

(i)           A = { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

Ans.   A = {x | x = n2, n ∊ N, n ≤ 10}

(ii)         B = { 6, 12, 18, 24, 30, 36, 42, 48}

Ans.   B = {x | x = 6 n, n ∊ N, n < 9}

(iii)       C = {S, M, I, L, E}

 Ans.  C = {S | S is a letter in the word ‘SMILE’}

(iv)        D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

  Ans.  D = {W | W is a day of a week}

(v)         X = {a, e, t}

  Ans.  X = {y | y is a letter in the word ‘eat’}

Types of sets

Singleton Set: - A set consisting of a single element is called a singleton set.

Empty Set or Null Set: - If there is not a single element in the set which satisfies the given Condition then it is called a Null set or an empty set. Null set is represented by { } or a symbol ф (phi).

Finite Set: - If a set is a null set or number of elements are limited and countable then it is called as ‘Finite set’.

Infinite Set: - If number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.

Equal sets: - Two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A.

'Set A and set B are equal sets', symbolically it is written as A = B.

Ex.  A = {x | x is a letter of the word ‘listen’.}

        ∴  A = { l, i, s, t, e, n}

B = {y | y is a letter of the word ‘silent’.}

     ∴  B = {s, i, l, e, n, t}

Though the elements of set A and B are not in the same order but all the elements are identical.

∴ A = B