**Chapter 1 Sets Practice Set 1.3**

Chapter 1 Sets Practice Set 1.3

**Question 1.If A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d}, D = {a, e}, then which of the following statements are true and which are false?i. C ⊆ 3ii. A ⊆ Diii. D ⊆ Biv. D ⊆ AV. B ⊆ Avi. C ⊆ AAnswer:**

i. C = {b, d}, B = {c, d, e ,f}

C ⊆ B

False

Since, all the elements of C are not present in B.

ii. A = {a, b, c, d, e}, D = {a, e}

A ⊆ D

False

Since, all the elements of A are not present in D.

iii. D = {a, e}, B = {c, d, e, f}

D ⊆ B

False

Since, all the elements of D are not present in B.

iv. D = {a, e}, A = {a, b, c, d, e}

D ⊆ A

True

Since, all the elements of D are present in A.

v. B = {c, d, e, f}, A = {a, b, c, d, e}

B ⊆ A

False

Since, all the elements of B are not present in A.

vi. C = {b, d}, A= {a, b, c, d, e}

C ⊆A

True

Since, all the elements of C are present in A.

**Question 2.Take the set of natural numbers from 1 to 20 as universal set and show set X and Y using Venn diagram. [2 Marks each]i. X= {x |x ∈ N, and 7 < x < 15}ii. Y = { y | y ∈ N, y is a prime number from 1 to 20}Answer:**

i. U = {1, 2, 3, 4, …….., 18, 19, 20}

x = {x | x ∈ N, and 7 < x < 15}

∴ x = {8, 9, 10, 11, 12, 13, 14}

ii. U = {1, 2, 3, 4, …… ,18, 19, 20}

Y = { y | y ∈ N, y is a prime number from 1 to 20}

∴ Y = {2, 3, 5, 7, 11, 13, 17, 19}

**Question 3.U = {1, 2, 3, 7, 8, 9, 10, 11, 12} P = {1, 3, 7,10}, theni. show the sets U, P and P’ by Venn diagram.ii. Verify (P’)’ = PSolution:**

i. Here, U = {1,2, 3, 7, 8,9, 10, 11, 12} P = {1, 3, 7, 10}

∴ P’ = {2, 8, 9, 11, 12}

II. Here, U = {1, 2, 3, 7, 8, 9, 10, 11, 12}

P = {1, 3, 7, 10} ….(i)

∴ P’= {2, 8, 9, 11, 12}

Also, (P’)’ = {1,3,7, 10} …(ii)

∴ (P’)’ = P … [From (i) and (ii)]

**Question 4.A = {1, 3, 2, 7}, then write any three subsets of A.Solution:**
Three subsets of A:

i. B = {3}

ii. C = {2, 1}

iii. D= {1, 2, 7}

[Note: The above problem has many solutions. Students may write solutions other than the ones given]

**Question 5.i. Write the subset relation between the sets.P is the set of all residents in Pune.M is the set of all residents in Madhya Pradesh.I is the set of all residents in Indore.B is the set of all residents in India.H is the set of all residents in Maharashtra.**

**ii. Which set can be the universal set for above sets ?Solution:**
i.

a. The residents of Pune are residents of India.

∴ P ⊆ B

b. The residents of Pune are residents of Maharashtra.

∴ P ⊆ H

c. The residents of Madhya Pradesh are residents of India.

∴ M ⊆ B

d. The residents of Indore are residents of India.

∴ I ⊆ B

e. The residents of Indore are residents of Madhya Pradesh.

∴ I ⊆ M

f. The residents of Maharashtra are residents of India.

∴ H ⊆B

ii. The residents of Pune, Madhya Pradesh, Indore and Maharashtra are all residents of India.

∴ B can be the Universal set for the above sets.

**Question 6.Which set of numbers could be the universal set for the sets given below?i. A = set of multiples of 5,B = set of multiples of 7,C = set of multiples of 12**

**ii. P = set of integers which are multiples of 4.T = set of all even square numbers.Answer:**

i. A = set of multiples of 5

∴ A = {5, 10, 15, …}

B = set of multiples of 7

∴ B = {7, 14, 21,…}

C = set of multiples of 12

∴ C = {12, 24, 36, …}

Now, set of natural numbers, whole numbers, integers, rational numbers are as follows:

N = {1, 2, 3, …}, W = {0, 1, 2, 3, …}

I = {…,-3, -2, -1, 0, 1, 2, 3, …}

Q = {

*pq*| p,q ∈ I,q ≠ 0}

Since, set A, B and C are the subsets of sets N, W , I and Q.

∴ For set A, B and C we can take any one of the set from N, W, I or Q as universal set.

ii. P = set of integers which are multiples of 4.

P = {4, 8, 12,…}

T = set of all even square numbers T = {2^{2}, 4^{2}, 6^{2}, …]

Since, set P and T are the subsets of sets N, W, I and Q.

∴ For set P and T we can take any one of the set from N, W, I or Q as universal set.

**Question 7.Let all the students of a class form a Universal set. Let set A be the students who secure 50% or more marks in Maths. Then write the complement of set A.Answer:**

Here, U = all the students of a class.

A = Students who secured 50% or more marks in Maths.

∴ A’= Students who secured less than 50% marks in Maths.

**Question 1.If A = {1, 3, 4, 7, 8}, then write all possible subsets of A.i. e. P = {1, 3}, T = {4, 7, 8}, V = {1, 4, 8}, S = {1, 4, 7, 8}In this way many subsets can be written. Write five more subsets of set A. (Textbook pg. no, 8)Answer:**
B = { },

E = {4},

C = {1, 4},

D = {3, 4, 7},

F = {3, 4, 7,8}

**Question 2.Some sets are given below.A ={…,-4, -2, 0, 2, 4, 6,…}B = {1, 2, 3,…}C = {…,-12, -6, 0, 6, 12, 18, }D = {…, -8, -4, 0, 4, 8,…}I = {…,-3, -2, -1, 0, 1, 2, 3, 4, }Discuss and decide which of the following statements are true.a. A is a subset of sets B, C and D.b. B is a subset of all the sets which are given above. (Textbook pg. no. 9)Solution:**
a. All elements of set A are not present in set B, C and D.

∴ A ⊆ B,

∴ A ⊆ C,

∴ A ⊆ D

∴ Statement (a) is false.

b. All elements of set B are not present in set A, C and D.

∴ B ⊆ A,

∴ B ⊆ C,

∴ B ⊆ D

∴ Statement (b) is false.

**Question 3.Suppose U = {1, 3, 9, 11, 13, 18, 19}, and B = {3, 9, 11, 13}. Find (B’)’ and draw the inference. (Textbook pg. no. 10)Solution:**
U = {1, 3, 9, 11, 13, 18, 19},

B= {3, 9, 11, 13} ….(i)

∴ B’= {1, 18, 19}

(B’)’= {3, 9, 11, 13} ….(ii)

∴ (B’)’ = B … [From (i) and (ii)]

∴ Complement of a complement is the given set itself.