# 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.

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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