# HOW TO CHECK IF THE GIVEN STATEMENT REPRESENTS SET

## About "How to Check if the Given Statement Represents Set"

How to Check if the Given Statement Represents Set :

Here we are going to see some practice questions on set theory.

## How to Check if the Given Statement Represents Set - Problems

Question 1 :

Which of the following are sets?

(i) The Collection of prime numbers upto 100.

Solution :

The above statement is well defined, the set will contain 2, 3, 5, 7, ..........97.

Hence it is a set.

(ii) The Collection of rich people in India.

Solution :

The set is not well defined. Hence it is not a set.

(iii) The Collection of all rivers in India.

Solution :

The statement is well defined. Hence it is a set.

(iv) The Collection of good Hockey players.

Solution :

The statement is not well defined. Hence it is not a set.

Question 2 :

List the set of letters of the following words in Roster form.

(i) INDIA (ii) PARALLELOGRAM

(iii) MISSISSIPPI (iv) CZECHOSLOVAKIA

Solution :

Now we have to write the letters of the given word. If we have repeated letters, then we have to write it once.

(i)  INDIA

A  =  {I, N, D, A}

(ii)  PARALLELOGRAM

B  =  {P, A, R, L, E, O, G, M}

(iii) MISSISSIPPI

C  =  {M, I, S, P}

(iv) CZECHOSLOVAKIA

D  =  {C, Z, E, H, O, S, L, V, A, K, I}

Question 3 :

Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and C = {12, 14,18, 20}.

(a) State whether True or False:

(i) 18 ∈ C (ii) 6 ∉ A (iii) 14  C (iv) 10  B

(v) 5  B (vi) 0  B

Solution :

(i) 18 ∈ C

18 is the element of set C, hence it is true.

(ii) 6 ∉ A

The set A does not contain the element 6, hence it is true.

(iii) 14  C

14 is the element of set C, hence the statement is false.

(iv) 10  B

10 is the element of set B, hence the statement is true.

(b) Fill in the blanks:

(i) 3  ____ (ii) 14  _____ (iii) 18 ____ B (iv) 4 _____ B

Solution :

3 is the element of set A, so  3  A.

14 is the element of set C, so 14  C.

18 is the element of set C, so 18  C.

4 is the element of set B, so   B.

After having gone through the stuff given above, we hope that the students would have understood, "How to Check if the Given Statement Represents Set".

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