Exercise 1.1 - Chapter 1 Set Language 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

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On April 24, 2024, 11:35 AM

Ex $1.1$ : Chapter 1 - Set Language - 9th Maths Guide Samacheer Kalvi Solutions
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.
Solution:
(i) $\mathrm{A}=\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83$, 89 and 97$\}$
As the collection of prime numbers upto 100 is known and can be counted (well defined). Hence this is a set.
(ii) The collection of rich people in India. Rich people has no definition.
Hence, it is not a set.
(iii) $\mathrm{A}=\{$ Cauvery, Sindhu, Ganga, $\}$
Hence, it is a set.
(iv) The collection of good hockey players is not a well - defined collection because the criteria for determining a hockey player's talent may vary from person to person.
Hence, this collection is not a set.

Question 2.
Listthe set of letters of the following words in Roster form.
(i) INDIA
(ii) PARALLELOGRAM
(iii) MISSISSIPPI
(iv) CZECHOSLOVAKIA
Solution:
(i) $\mathrm{A}=\{\mathrm{I}, \mathrm{N}, \mathrm{D}, \mathrm{A}\}$
(ii) $\mathrm{B}=\{\mathrm{P}, \mathrm{A}, \mathrm{R}, \mathrm{L}, \mathrm{E}, \mathrm{O}, \mathrm{G}, \mathrm{M}\}$
(iii) $\mathrm{C}=\{\mathrm{M}, \mathrm{I}, \mathrm{S}, \mathrm{P}\}$
(iv) $\mathrm{D}=\{\mathrm{C}, \mathrm{Z}, \mathrm{E}, \mathrm{H}, \mathrm{O}, \mathrm{S}, \mathrm{L}, \mathrm{V}, \mathrm{A}, \mathrm{K}, \mathrm{I}\}$.

Question $3 .$
Consider the following sets $\mathrm{A}=\{0,3,5,8\} \mathrm{B}=\{2,4,6,10\} \mathrm{C}=\{12,14,18,20\}$
(a) State whether True or false.
(i) $18 \in \mathrm{C}$
(ii) $6 \notin \mathrm{A}$
(iii) $14 \notin \mathrm{C}$
(iv) $10 \in \mathrm{B}$
(v) $5 \in B$
(vi) $0 \in B$
(b) Fill in the blanks?
(i) $3 \in$
(ii) $14 \mathrm{e}$
(iii) 18
(iv) $4 \ldots B$
Solution:
(a) (i) True
(ii) True
(iii) False
(iv) True
(v) False
(vi) False,

(b) (i) $\mathrm{A}$
(ii) $\mathrm{C}$
(iii) $\notin$
(iv) $\in$

Question $4 .$
Represent the following sets in Roster form.
(i) $\mathrm{A}=$ The set of all even natural numbers less than 20 .
(ii) $\mathrm{B}=\left\{\mathrm{y}: \mathrm{y}=\frac{1}{2 n}, \mathrm{n} \in \mathrm{N}, \mathrm{n} \leq 5\right\}$
(iii) $\mathrm{C}=(\mathrm{x}: \mathrm{x}$ is perfect cube, $27<\mathrm{x}<216\}$
(iv) $\mathrm{D}=\{\mathrm{x}: \mathrm{x} \in \mathrm{Z},-5<\mathrm{x} \leq 2\}$
Solution:
(i) $\mathrm{A}=\{2,4,6,8,10,12,14,16,18\}$
(ii) $\mathrm{N}=\{1,2,3,4,5\}$

$\text { if, } \begin{aligned}
n &=1, y=\frac{1}{2 n}=\frac{1}{2 \times 1}=\frac{1}{2} \\
n &=2, y=\frac{1}{2 \times 2}=\frac{1}{4} \\
n &=3, y=\frac{1}{2 \times 3}=\frac{1}{6} \\
n &=4, y=\frac{1}{2 \times 4}=\frac{1}{8} \\
n &=5, y=\frac{1}{2 \times 5}=\frac{1}{10} \\
\therefore \mathrm{B} &=\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \frac{1}{10}\right\}
\end{aligned}$
(iii) $\mathrm{C}=\{64,125\}$
(iv) $\mathrm{D}=\{-4,-3,-2,-1,0,1,2\}$
 

Question $5 .$
Represent the following sets in set builder form.
(i) $\mathrm{B}=$ The set of all Cricket players in India who scored double centuries in One Day Internationals.
(ii) $\mathrm{C}=\left\{\frac{1}{2}, \frac{2}{3}, \frac{3}{4} \ldots .\right\}$.
(iii) $\mathrm{D}=$ The set of all tamil months in a year.
(iv) $\mathrm{E}=$ The set of odd Whole numbers less than 9 .
Solution:
(i) $\mathrm{B}=\{\mathrm{x}: \mathrm{x}$ is an Indian player who scored double centuries in one day internationals $\}$
(ii) $\mathrm{C}=\left\{\mathrm{x}: \mathrm{x}=\frac{n}{n+1}, \mathrm{n} \in \mathrm{N}\right\}$
(iii) $\mathrm{D}=\{\mathrm{x}: \mathrm{x}$ is a tamil month in a year $\}$
(iv) $\mathrm{E}=\{\mathrm{x}: \mathrm{x}$ is odd number, $\mathrm{x} \in \mathrm{W}, \mathrm{x}<9$, where $\mathrm{W}$ is the set of whole numbers $\}$.
 

Question 6.
Represent the following sets in descriptive form.
(i) $\mathrm{P}=\{$ January, June, July $\}$
(ii) $\mathrm{Q}=\{7,11,13,17,19,23,29\}$
(iii) $\mathrm{R}=\{\mathrm{x}: \mathrm{x} \in \mathrm{N}, \mathrm{x}<5\}$
(iv) $\mathrm{S}=\{\mathrm{x}: \mathrm{x}$ is a consonant in English alphabets $\}$
Solution:

(i) $\mathrm{P}$ is the set of English Months begining with $\mathrm{J}$.
(ii) $Q$ is the set of all prime numbers between 5 and 31 .
(iii) $R$ is the set of all natural numbers less than 5 .
(iv) $S$ is the set of all English consonants.