HOW TO CHECK IF THE GIVEN STATEMENT REPRESENTS SET

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  4 ∈ B.

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