Worksheet on Properties of a Set

Practice the set of questions given in the worksheet on properties of a set.

1. State which of the following are true:

(i) 2 ∈ N

(ii) 0 ∈ N

(iii) -2 ∉ I

(iv) 0 ∈ I

(v) -5 ∉ W

(vi) 7 ∈ W


2. Let A = {1, 3, 5, 7, 9}. Insert A or ∈ or ∉.

(i) 1 ______ A

(ii) 6 ______ A

(iii) 9 ______ A 

(iv) 2 ∉ ______

(v) 3 ∈ ______


3. State which of the following are false:

(i) a ∈ {a, e, i, o, u}

(ii) v ∈ {a, e, i, o, u}

(iii) 2 ∉ {x | x is an even number}

(iv) {p} ∈ {p, q, r}

(v) {p, q} ∉ {p, q, r}

 

4. If set A = {2, 3, 4, 5, 6}.

State, whether the following statements are true or false:

(i)  2 ∈ A

(ii) 5, 6 ∈ A

(iii) 3, 4, 7 ∈ A

(iv) 2, 8 ∈ A


5. (i) 5 ∈ B

(ii) 12 ∈ B

(iii) 14 ∈ B

(iv) 9 ∈ B

(v) B is a set of even numbers between 2 and 16.

(vi) 4, 6 and 10 are members of the set B.

 

6. Two sets P and Q are given as follows:

P = {3, 5, 7, 9, 11, 13} and Q = {8, 10, 12, 14, 16, 18}

State, given reasons, which of the following are true:

(i) 13 ∈ P, 9 ∈ P but 13 + 9 ∉ P.

(ii) 5 ∈ P, 7 ∈ P and 5 + 7 ∈ Q.

(iii) 3 ∈ P, 13 ∈ P but 13 - 3 ∉ Q.

(iv) 7 ∉ Q,  9 ∉ Q but 7 + 9 ∈ Q.


Answers for the worksheet on properties of a set are given below to check the exact answers of the above questions related to set.


Answers:


1. (i) True

(ii) False

(iii) False

(iv) True

(v) True

(vi) True


2.  (i) ∈

(ii) ∉

(iii) ∈

(iv) A

(v) A


3. (i) True

(ii) False

(iii) False

(iv) False

(v) True

 

4. (i)  True

(ii) True

(iii) False

(iv) False


5. If set B = {4, 6, 8, 10, 12, 14}.

State, which of the following statements are correct and which are wrong and also write the wrong statements correctly:

(i) Wrong; 5 ∉ B

(ii) Correct

(iii) Correct

(iv) Wrong; 9 ∉ B

(v) Correct

(vi) Correct


6.  (i) True : 13 + 9 = 22, which is not in set P.

(ii) True : 5 + 7 = 12, which is in set Q.

(iii) False.

(iv) True : 7 + 9 = 16, which belongs to set Q.

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