EXERCISE:5.1
Question 1
i) All state of india
ii) Last three days of a week
iii) All months of a year having atleast 30 days
The above three are set because they are well defined
Remaining all are not sets, they are not well defined
Question 2
(iii) and (iv) are two
(i) is false because C is not a vowel
(ii) is false because {a} is a set and not element
(iii) is false because b is not vowel , so $b \notin A$ of course , $a \in A$
(v) is false , {a,i ,u} is a set and not elements
Question 3
(i)The set of first six letters of alphabet
ii) {prime numbers less than 20 }
iii) {last three days of a weet }
iv) {months of a year whose name being with a vowel}
Question 4
i) $\{12,14,16,18,20,22 \ldots \ldots, 48\}$ ;$\{x: x=2 n, n \in N$ and $5<n<25$}
ii) { Jan, Mar, may, July, Aug, oct, Dec }
{$x \mid x$ is a month of a year having more than 30 days}
iii) {0,1,4,9},{x $\mid x$ is a perfect square one digit number}
iv) {1,2,3,4,6,9,12,18,36} ;{x $\mid x$ is a factrr of 36}
Question 5
i) {0,4,8 ,8,12,16}; {whole numbers which are divisible by 4 and less than 20}
ii) {1,4,9,16,25,36,49};{square of first seven natural number}
iii) {-1,1,3,5,7};{odd integers which lie between -2 and 8}
iv) {U,L,T,I,M,A};{letters in the word ULTIMATUM}
Question 6
i) $\{5,6,7,8,9\}$
ii) $\{-12,-6,0,6,12\}$
iii) $\{0,3,8,15\}$
iv) $\{1\}$
V) $\{N, T\}$
vi) $\{1,0,5,6,7\}$
Question 7
i) {x:x is an odd natural number and $x<30$}
ii) {$x \mid x$ is a prime number and $x<30$}
iii) $\left\{x \mid x=n^{2}, n \in N\right\}$
iv) $\left\{x \mid x=\frac{1}{n}, \quad \eta \in N\right.$ and $\left.5 \leq n \leq 20\right\}$
v) $\{x \mid x=s p, p \in I$ and $-2 \leq p \leq 5\}$
vi) $\{x: x$ is a month of a year whose name beings with letter 'J'
Question 8
i) {Vowels in the word COMPETITION}
ii) {x: x is a vowel in the word COMPETITION}
iii) {O,E,I}
EXERCISE:5.2
Question 1
i) Finite set having seven colours
ii)Empty set , having no element in between
iii) Infinite set , having infinite elements
iv) Infinite set
v) Finite set, Having finite digits i.e 6
vi)Finite set, having 6 letters
vii)Infinite Set , have infinite numbers
viii)Finite set , have 8 prime factors
ix) Empty set, have no vowel in the word
x)Finite set , 12 element in it .
Question 2
(i),(ii),(iii),(iv) represent same sets
(iv) is different from other sets
Question 3
A, B and E are equal
C,F and H are equal
D and G are equal
Question 4
A, C , E and G are equivalent , These are having 7 elements
B and D are equivalent , having 3 element
F and H are equivalent , having 12 element
I and J are equivalent , having 52 elements
Question 5
i) $A \subset B, B C A, A=B$
ii) $A \subset B$ but $B \& A$
iii) $B \subset A$ but $A \subset B$
iv) neither $A \subset B$ nor $B \subset A$
Question 6
i) False
ii) False
iii) True, because there are 5 elements in each
Question 7
i) $\phi$
ii) $\phi,\{3\},\{5\},\{3,5\}$
iii) $\phi,\{2\},\{4\},\{6\},\{2,4\},\{4,6\},\{2,6\}$,{2,4,6}
Question 8
i) $\xi=N$
$A=\{2,4,6,8\}$
ii) $\quad \xi=W$
$A=\{0,2,4,6,8\}$
iii) $\xi=d$
$A=\{\ldots,-4,-2,0,2,4,6,8\}$
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