Samacheer Kalvi Class 9 Maths Solutions Chapter 1 Set Language Exercise 1.1

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.1

Question 1. Which of the following are sets?
(i) The collection of prime numbers upto 100
(ii) The collection of rich people in India
(iii) The collection of all rivers in India
(iv) The collection of good hockey players
Answer:
(i) It is a set. (The collection of prime numbers up to 100 is clearly defined and we can list all its elements.)
(ii) It is not a set. (The word "rich" is not clearly defined; what one person considers rich, another might not.)
(iii) It is a set. (The collection of all rivers in India is a well-defined group, even though it's very large.)
(iv) It is not a set. (The word "good" is subjective and not well-defined, so different people would choose different players.)
In simple words: A collection is a "set" if you can clearly tell what belongs in it and what does not. If the description is vague or depends on opinion, it's not a set.

🎯 Exam Tip: To determine if a collection is a set, always check if its elements can be defined objectively without personal opinion or ambiguity. Use the "well-defined" criteria.

Question 2. List the set of letters of the following words in Roster form.
(i) INDIA
(ii) PARALLELOGRAM
(iii) MISSISSIPPI
(iv) CZECHOSLOVAKIA
Answer:
(i) \( A = \{I, N, D, A\} \)
(ii) \( B = \{P, A, R, L, E, O, G, M\} \)
(iii) \( C = \{M, I, S, P\} \)
(iv) \( D = \{C, Z, E, H, O, S, L, V, A, K, I\} \) Each letter appears only once in the set, even if it repeats in the word.
In simple words: To write a set in Roster form, list all the unique letters from the word inside curly brackets. Don't write any letter more than once, even if it appears many times in the word.

🎯 Exam Tip: Remember that in Roster form, elements are listed only once, and the order of elements does not matter.

Question 3. Consider the following sets \( A = \{0, 3, 5, 8\} \), \( B = \{2, 4, 6, 10\} \) and \( C = \{12, 14, 18, 20\} \).
(a) State whether True or False:
(i) \( 18 \in C \)
(ii) \( 6 \notin A \)
(iii) \( 14 \notin C \)
(iv) \( 10 \in B \)
(v) \( 5 \in B \)
Answer:
(i) True. (18 is an element of set C)
(ii) True. (6 is not an element of set A)
(iii) False. (14 is an element of set C, so \( 14 \notin C \) is incorrect)
(iv) True. (10 is an element of set B)
(v) False. (5 is not an element of set B, it is in set A)
In simple words: The symbol \( \in \) means "is an element of" and \( \notin \) means "is not an element of". We check if the number is inside the given set.

🎯 Exam Tip: Pay close attention to the symbols \( \in \) and \( \notin \), and carefully check each number against the specified set to determine truthfulness.

Question 3. (b) Fill in the blanks:
(i) 3 \( \in \) ............
(ii) 14 \( \in \) ............
(iii) 18 ............ B
(iv) 4 ............ B
Answer:
(i) A
(ii) C
(iii) \( \notin \)
(iv) \( \in \) We use the correct symbol or set name based on where the number belongs.
In simple words: For the blanks, write the set name if the number belongs to it. If a number is not in a set, use the "not an element of" symbol (\( \notin \)).

🎯 Exam Tip: Double-check the elements of each set to accurately fill in the blanks with the correct set or membership symbol.

Question 4. Represent the following sets in Roster form.
(i) A = The set of all even natural numbers less than 20.
(ii) B = \( \{y : y = \frac{1}{2n}, n \in N, n \le 5\} \)
(iii) C = \( \{x : x \) is perfect cube, \( 27 < x < 216\} \)
(iv) D = \( \{x : x \in Z, – 5 < x \le 2\} \)
Answer:
(i) \( A = \{2, 4, 6, 8, 10, 12, 14, 16, 18\} \)
(ii) \( B = \{\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \frac{1}{10}\} \) We find these values by putting \( n = 1, 2, 3, 4, 5 \) into the formula \( \frac{1}{2n} \).
(iii) \( C = \{64, 125\} \) Perfect cubes between 27 and 216 are \( 4^3 = 64 \) and \( 5^3 = 125 \).
(iv) \( D = \{-4, -3, -2, -1, 0, 1, 2\} \) These are all the integers (Z) greater than -5 and less than or equal to 2.
In simple words: Roster form means listing all the elements inside curly brackets. For set builder notation, you need to understand the rule and list all the numbers that fit it.

🎯 Exam Tip: For set builder notation, carefully identify the type of numbers (natural, integer, whole) and the conditions (e.g., less than, greater than, perfect cube) to list the correct elements.

Question 5. Represent the following sets in set builder form.
(i) B = The set of all cricket players in India who scored double centuries in one day internationals.
(ii) C = \( \{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, .......\} \)
(iii) D = The set of all Tamil months in a year.
(iv) E = The set of odd Whole numbers less than 9.
Answer:
(i) \( B = \{x : x \) is a cricket player in India who scored double centuries in one day internationals\( \} \)
(ii) \( C = \{x : n \in N, x = \frac{n}{n + 1}\} \) Here, 'n' represents natural numbers, and each term follows the pattern of n divided by (n+1).
(iii) \( D = \{x : x \in \) set of all Tamil months in a year\( \} \)
(iv) \( E = \{x : x \) is an odd whole number and \( x < 9\} \)
In simple words: Set builder form describes the rule that all elements in the set follow, rather than listing them one by one. It tells you what kind of item 'x' is and what conditions 'x' must meet.

🎯 Exam Tip: When writing in set builder form, ensure the description is precise and covers all elements of the set without including any extra ones. Define the variable and its properties clearly.

Question 6. Represent the following sets in descriptive form.
(i) P = { January, June, July}
(ii) Q = {7, 11, 13, 17, 19, 23, 29}
(iii) R = \( \{x: x \in N, x < 5\} \)
(iv) S = \( \{x : x \) is a consonant in English alphabets\( \} \)
Answer:
(i) P = The set of all months beginning with the letter "J". This describes all months that start with J.
(ii) Q = The set of all prime numbers between 5 and 31. These are all the prime numbers that fall in that range.
(iii) R = The set of natural numbers less than 5. Natural numbers start from 1, so this means 1, 2, 3, 4.
(iv) S = The set of consonants in English alphabets. Consonants are all letters that are not vowels.
In simple words: Descriptive form means explaining what the set is in simple words. You write a sentence that tells someone exactly what kind of things are in the set.

🎯 Exam Tip: For descriptive form, use clear and concise language that accurately defines the set's contents without listing individual elements.