Sets

NCERT Class 11 Maths • Exercise 1.1

1. Identifying Sets (Well-defined Collections)

Q1: Which of the following are sets? Justify.

(i) Collection of months beginning with ‘J’

Well-defined: {January, June, July}. We can definitely decide if a month belongs or not.
Answer: Set

(ii) Collection of ten most talented writers of India

Not well-defined: “Talented” is subjective. One person’s choice may differ from another’s.
Answer: Not a Set

(iii) Team of eleven best-cricket batsmen of the world

Not well-defined: “Best” is subjective and varies from person to person.
Answer: Not a Set

(iv) Collection of all boys in your class

Well-defined: We can identify exactly who belongs to the class.
Answer: Set

(v) Collection of all natural numbers less than 100

Well-defined: {1, 2, 3, …, 99}.
Answer: Set

(vi) Collection of novels written by Munshi Prem Chand

Well-defined: We can list exactly the specific books written by him.
Answer: Set

(vii) Collection of all even integers

Well-defined: {…, -4, -2, 0, 2, 4, …}.
Answer: Set

(viii) Collection of questions in this Chapter

Well-defined: We can identify if a question belongs to this chapter or not.
Answer: Set

(ix) Collection of most dangerous animals of the world

Not well-defined: “Dangerous” is vague (size? venom? aggression?).
Answer: Not a Set

2. Insert Symbol ($\in$ or $\notin$)

Let $A = \{1, 2, 3, 4, 5, 6\}$

Q2: Fill in the blanks with $\in$ or $\notin$.
  • (i) $5 \dots A \rightarrow$ $\in$ (5 is in A)
  • (ii) $8 \dots A \rightarrow$ $\notin$ (8 is not in A)
  • (iii) $0 \dots A \rightarrow$ $\notin$
  • (iv) $4 \dots A \rightarrow$ $\in$
  • (v) $2 \dots A \rightarrow$ $\in$
  • (vi) $10 \dots A \rightarrow$ $\notin$

3. Roster Form

Q3: Write the following sets in roster form.

(i) $A = \{x : x \text{ is an integer and } -3 \le x < 7\}$

Integers starting from -3 up to (but not including) 7.
$A = \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$

(ii) $B = \{x : x \text{ is a natural number less than } 6\}$

$B = \{1, 2, 3, 4, 5\}$

(iii) $C = \{x : x \text{ is a two-digit natural number such that sum of digits is } 8\}$

Combinations: 1+7, 2+6, 3+5, 4+4, 5+3, 6+2, 7+1, 8+0.
$C = \{17, 26, 35, 44, 53, 62, 71, 80\}$

(iv) $D = \{x : x \text{ is a prime number which is divisor of } 60\}$

Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Prime divisors: 2, 3, 5.
$D = \{2, 3, 5\}$

(v) $E = \text{The set of all letters in the word TRIGONOMETRY}$

Distinct letters only.
$E = \{T, R, I, G, O, N, M, E, Y\}$

(vi) $F = \text{The set of all letters in the word BETTER}$

Distinct letters only.
$F = \{B, E, T, R\}$

4. Set-Builder Form

Q4: Write in set-builder form.

(i) $\{3, 6, 9, 12\}$

Multiples of 3.
$\{x : x = 3n, n \in N \text{ and } 1 \le n \le 4\}$

(ii) $\{2, 4, 8, 16, 32\}$

Powers of 2 ($2^1$ to $2^5$).
$\{x : x = 2^n, n \in N \text{ and } 1 \le n \le 5\}$

(iii) $\{5, 25, 125, 625\}$

Powers of 5 ($5^1$ to $5^4$).
$\{x : x = 5^n, n \in N \text{ and } 1 \le n \le 4\}$

(iv) $\{2, 4, 6, \dots\}$

Set of all even natural numbers.
$\{x : x \text{ is an even natural number}\}$

(v) $\{1, 4, 9, \dots, 100\}$

Squares of numbers ($1^2$ to $10^2$).
$\{x : x = n^2, n \in N \text{ and } 1 \le n \le 10\}$

5. Listing Elements

Q5: List all elements.

(i) $A = \{x : x \text{ is an odd natural number}\}$

$A = \{1, 3, 5, 7, \dots\}$

(ii) $B = \{x : x \text{ is an integer, } -\frac{1}{2} < x < \frac{9}{2}\}$

$-0.5 < x < 4.5$. Integers are 0, 1, 2, 3, 4.
$B = \{0, 1, 2, 3, 4\}$

(iii) $C = \{x : x \text{ is an integer, } x^2 \le 4\}$

Integers whose square is $\le 4$ are -2, -1, 0, 1, 2.
$C = \{-2, -1, 0, 1, 2\}$

(iv) $D = \{x : x \text{ is a letter in the word LOYAL}\}$

$D = \{L, O, Y, A\}$

(v) $E = \{x : x \text{ is a month not having 31 days}\}$

$E = \{\text{February, April, June, September, November}\}$

(vi) $F = \{x : x \text{ is a consonant preceding k}\}$

Letters before k: a, b, c, d, e, f, g, h, i, j.
Remove vowels (a, e, i).
$F = \{b, c, d, f, g, h, j\}$

6. Matching Roster to Set-Builder

Q6: Match the sets.
Roster Form Set-Builder Form
(i) $\{1, 2, 3, 6\}$ (c) $\{x : x \text{ is natural number and divisor of 6}\}$
(ii) $\{2, 3\}$ (a) $\{x : x \text{ is a prime number and a divisor of 6}\}$
(iii) $\{M,A,T,H,E,I,C,S\}$ (d) $\{x : x \text{ is a letter of the word MATHEMATICS}\}$
(iv) $\{1, 3, 5, 7, 9\}$ (b) $\{x : x \text{ is an odd natural number less than 10}\}$
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