# 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.

Sets and Venn-diagrams Worksheets

Worksheet on Set

Worksheet on Elements Form a Set

Worksheet to Find the Elements of Sets

Worksheet on Properties of a Set

Worksheet on Sets in Roster Form

Worksheet on Sets in Set-builder Form

Worksheet on Finite and Infinite Sets

Worksheet on Equal Sets and Equivalent Sets

Worksheet on Empty Sets

Worksheet on Subsets

Worksheet on Union and Intersection of Sets

Worksheet on Disjoint Sets and Overlapping Sets

Worksheet on Difference of Two Sets

Worksheet on Operation on Sets

Worksheet on Cardinal Number of a Set

Worksheet on Venn Diagrams

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