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Q5(iv):
List all the elements of the following sets : (iv) $D = \{x : x$ is a letter in the word “LOYAL”\}
Solution :
Step 1: Definition of a Set in Roster Form
In set theory, a set is defined as a well-defined collection of distinct objects. When representing a set in Roster (or Tabular) form, every unique element of the set is listed exactly once, separated by commas, and enclosed within curly brackets $\{ \}$. [Per the principles of Zermelo-Fraenkel set theory regarding the extensionality of sets].
Step 2: Analyzing the Given Word
The given condition defines set $D$ as containing the letters of the word "LOYAL". We must perform a lexicographical breakdown of the word to identify individual letters:
- Letter 1: L
- Letter 2: O
- Letter 3: Y
- Letter 4: A
- Letter 5: L
Step 3: Applying the Law of Uniqueness
A fundamental property of sets is that elements must be distinct. If an element is repeated in the descriptive criteria, it appears only once in the roster representation [By the Axiom of Specification].
| Character | Status |
|---|---|
| L | Included |
| O | Included |
| Y | Included |
| A | Included |
| L | Excluded (Duplicate) |
Step 4: Construction of the Set
By collecting the unique identifiers identified in Step 3, we construct the set $D$:
$D = \{L, O, Y, A\}$
Final Solution: $D = \{L, O, Y, A\}$
More Questions from Class 11 Mathematics Sets EXERCISE 1.1
- Q1(i): Which of the following are sets ? Justify your answer. (i) The collection of all the months of a year beginning with the letter J.
- Q1(ii): Which of the following are sets ? Justify your answer. (ii) The collection of ten most talented writers of India.
- Q1(iii): Which of the following are sets ? Justify your answer. (iii) A team of eleven best-cricket batsmen of the world.
- Q1(iv): Which of the following are sets ? Justify your answer. (iv) The collection of all boys in your class.
- Q1(ix): Which of the following are sets ? Justify your answer. (ix) A collection of most dangerous animals of the world.
- Q1(v): Which of the following are sets ? Justify your answer. (v) The collection of all natural numbers less than 100.
- Q1(vi): Which of the following are sets ? Justify your answer. (vi) A collection of novels written by the writer Munshi Prem Chand.
- Q1(vii): Which of the following are sets ? Justify your answer. (vii) The collection of all even integers.
- Q1(viii): Which of the following are sets ? Justify your answer. (viii) The collection of questions in this Chapter.
- Q2(i): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (i) 5. . .A
- Q2(ii): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (ii) 8 . . . A
- Q2(iii): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (iii) 0. . .A
- Q2(iv): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (iv) 4. . . A
- Q2(v): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (v) 2. . .A
- Q2(vi): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (vi) 10. . .A
- Q3(i): Write the following sets in roster form: (i) $A = \{x : x$ is an integer and $–3 \le x < 7\}$
- Q3(ii): Write the following sets in roster form: (ii) $B = \{x : x$ is a natural number less than 6\}
- Q3(iii): Write the following sets in roster form: (iii) $C = \{x : x$ is a two-digit natural number such that the sum of its digits is 8\}
- Q3(iv): Write the following sets in roster form: (iv) $D = \{x : x$ is a prime number which is divisor of 60\}
- Q3(v): Write the following sets in roster form: (v) $E$ = The set of all letters in the word TRIGONOMETRY
- Q3(vi): Write the following sets in roster form: (vi) $F$ = The set of all letters in the word BETTER
- Q4(i): Write the following sets in the set-builder form : (i) $\{3, 6, 9, 12\}$
- Q4(ii): Write the following sets in the set-builder form : (ii) $\{2,4,8,16,32\}$
- Q4(iii): Write the following sets in the set-builder form : (iii) $\{5, 25, 125, 625\}$
- Q4(iv): Write the following sets in the set-builder form : (iv) $\{2, 4, 6, . . .\}$
- Q4(v): Write the following sets in the set-builder form : (v) $\{1,4,9, . . .,100\}$
- Q5(i): List all the elements of the following sets : (i) $A = \{x : x$ is an odd natural number\}
- Q5(ii): List all the elements of the following sets : (ii) $B = \{x : x$ is an integer, $– \frac{1}{2} < x < \frac{9}{2}\}$
- Q5(iii): List all the elements of the following sets : (iii) $C = \{x : x$ is an integer, $x^2 \le 4\}$
- Q5(v): List all the elements of the following sets : (v) $E = \{x : x$ is a month of a year not having 31 days\}
- Q5(vi): List all the elements of the following sets : (vi) $F = \{x : x$ is a consonant in the English alphabet which precedes $k$ \}.
- Q6: Match each of the set on the left in the roster form with the same set on the right described in set-builder form: (i) $\{1, 2, 3, 6\}$ (a) $\{x : x$ is a prime number and a divisor of 6\} (ii) $\{2, 3\}$ (b) $\{x : x$ is an odd natural number less than 10\} (iii) $\{M,A,T,H,E,I,C,S\}$ (c) $\{x : x$ is natural number and divisor of 6\} (iv) $\{1, 3, 5, 7, 9\}$ (d) $\{x : x$ is a letter of the word MATHEMATICS\}.
CBSE Solutions for Class 11 Mathematics Sets
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