Maharashtra Board Class 9 Maths Chapter 1 Set 1.1 Algebra Standard Part 1 Sets Solutions

Question 1. Write the following sets in roster form.
(i) Set of even natural numbers
(ii) Set of even prime numbers from 1 to 50
(iii) Set of negative integers
(iv) Seven basic sounds of a sargam (sur)
Answer:
(i) \( A = \{2, 4, 6, 8, \dots\} \)
(ii) \( B = \{2\} \)
(iii) \( C = \{-1, -2, -3, \dots\} \)
(iv) \( D = \{\text{Sa}, \text{Re}, \text{Ga}, \text{Ma}, \text{Pa}, \text{Dha}, \text{Ni}\} \)
These sets represent standard mathematical collections and musical notes written clearly inside curly brackets.
In simple words: Roster form means listing all the members of a set inside curly brackets, separated by commas. For example, even numbers are listed as 2, 4, 6, and so on, while the only even prime number is 2.

🎯 Exam Tip: Always use curly brackets \( \{ \} \) for roster form and separate the elements with commas. Do not forget to use dots \( \dots \) for infinite sets to show they continue forever.

Question 2. Write the following symbolic statements in words.
(i) \( \frac{4}{3} \in Q \)
(ii) \( -2 \notin N \)
(iii) \( P = \{p \mid p \text{ is an odd number}\} \)
Answer:
(i) \( \frac{4}{3} \) is an element of set Q.
(ii) -2 is not an element of set N.
(iii) Set P is a set of all p’s such that p is an odd number. This notation helps us describe sets clearly using mathematical symbols.
In simple words: We are translating math symbols into normal English sentences. For example, the symbol \( \in \) means "is a member of" or "belongs to".

🎯 Exam Tip: Pay close attention to the slash in the membership symbol (\( \notin \)), which represents negation ("is not an element of"). Always write the set names in capital letters.

Question 3. Write any two sets by listing method and by rule method.
Answer:
(i) A is a set of even natural numbers less than 10.
Listing method: \( A = \{2, 4, 6, 8\} \)
Rule method: \( A = \{x \mid x = 2n, n \in N, n < 5\} \)

(ii) B is a set of letters of the word ‘SCIENCE’.
Listing method: \( B = \{S, C, I, E, N\} \)
Rule method: \( B = \{x \mid x \text{ is a letter of the word 'SCIENCE'}\} \). Both methods are equally valid ways to represent the exact same mathematical set.
In simple words: Listing method means writing down every single member of the set inside curly brackets. Rule method means writing a formula or description that explains who is allowed in the set.

🎯 Exam Tip: In the listing method, remember that elements are never repeated, and their order does not matter. Always use curly brackets \( \{ \} \) for sets.

Question 4. Write the following sets using listing method.
(i) All months in the Indian solar year.
(ii) Letters in the word ‘COMPLEMENT’.
(iii) Set of human sensory organs.
(iv) Set of prime numbers from 1 to 20.
(v) Names of continents of the world.
Answer:
(i) \( A = \{\text{Chaitra, Vaishakh, Jyestha, Aashadha, Shravana, Bhadrapada, Ashwina, Kartika, Margashirsha, Paush, Magha, Falguna}\} \)
(ii) \( X = \{C, O, M, P, L, E, N, T\} \)
(iii) \( Y = \{\text{Nose, Ears, Eyes, Tongue, Skin}\} \)
(iv) \( P = \{2, 3, 5, 7, 11, 13, 17, 19\} \)
(v) \( C = \{\text{Asia, Africa, North America, South America, Antarctica, Europe, Australia}\} \). Listing these elements clearly shows the complete membership of each defined group.
In simple words: We are listing out all the individual items that belong to each group, making sure not to repeat any letters or items.

🎯 Exam Tip: When listing letters of a word like 'COMPLEMENT', make sure to write repeating letters (like 'E' and 'M') only once in your final set.

Question 5. Write the following sets using rule method.
(i) \( A = \{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\} \)
(ii) \( B = \{6, 12, 18, 24, 30, 36, 42, 48\} \)
(iii) \( C = \{S, M, I, L, E\} \)
(iv) \( D = \{\text{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}\} \)
(v) \( X = \{a, e, t\} \)
Answer:
(i) \( A = \{x \mid x = n^2, n \in \mathbb{N}, n \le 10\} \)
(ii) \( B = \{x \mid x = 6n, n \in \mathbb{N}, n < 9\} \)
(iii) \( C = \{y \mid y \text{ is a letter of the word 'SMILE'}\} \) [Other possible words: 'SLIME', 'MILES', 'MISSILE' etc.]
(iv) \( D = \{z \mid z \text{ is a day of the week}\} \)
(v) \( X = \{y \mid y \text{ is a letter of the word 'eat'}\} \) [Other possible words: 'tea' or 'ate']
In simple words: Rule method describes a set by stating the common property of its elements rather than listing them all. For example, instead of listing square numbers, we write the formula that generates them.

🎯 Exam Tip: When writing sets in rule method, clearly define the variable, its formula or property, and the set of numbers (like natural numbers) it belongs to.

Question 1. Fill in the blanks given in the following table. (Textbook pg. no. 3)
Answer:

In simple words: This table shows how the same set of numbers or items can be written in two different ways: by listing every single item, or by writing a rule that describes them.

🎯 Exam Tip: Pay close attention to the boundaries of the sets (like "between 1 to 20" or "-3 < x < 3") to ensure you don't include or exclude elements incorrectly.