Exercise 1.7 - Chapter 1 Set Language 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $1.7$
Multiple Choice Questions
Question $1 .$
Which of the following is correct?
(1) $\{7\} \in\{1,2,3,4,5,6,7,8,9,10\}$
(2) $7 \in\{1,2,3,4,5,6,7,8,9,10\}$
(3) $7 \notin\{1,2,3,4,5,6,7,8,9,10\}$
(4) $\{7\} \nsubseteq\{1,2,3,4,5,6,7,8,9,10\}$
Solution:
(2) $7 \in\{1,2,3,4,5,6,7,8,9,10\}$

Question $2 .$
The set $P=\{x \mid x \in Z,-1 (1) Singleton set
(2) Power set
(3) Null set
(4) Subset
Solution:
(1) Singleton set
Hint: $\mathbf{P}=\{0\}$

Question $3 .$
If $U=\{x \mid x \in N, x<10\}$ and $A=\{x \mid x \in N, 2 \leq x<6\}$ then (A') ' is
(1) $\{1,6,7,8,9\}$
(2) $\{1,2,3,4\}$
(3) $\{2,3,4,5\}$
Solution:
(3) $\{2,3,4,5\}$
Hint: $\left(A^{\prime}\right)=A=\{2,3,4,5\}$

Question $4 .$
If $B \subseteq A$ then $n(A \cap B)$ is
(1) $n(A-B)$
(2) $\mathrm{n}(\mathrm{B})$
(3) $n(B-A)$
(4) $\mathrm{n}(\mathrm{A})$
Solution:
(2) $\mathrm{n}(\mathrm{B})$
Hint: $B \subseteq A \Rightarrow A \cap B=B$
 

Question $5 .$
If $A=\{x, y, z\}$ then the number of non-empty subsets of $A$ is
(1) 8
(2) 5
(3) 6
(4) 7
Solution:
(4) 7
Hint: Number of non-empty subsets $=2-1=8-1=7$
 

Question 6 .
Which of the following is correct ?
(1) $\emptyset \subseteq\{a, b\}$
(2) $\emptyset \in\{a, b\}$
(3) $\{a\} \in\{a, b\}$
(4) $a \subseteq\{a, b\}$
Solution:
(1) $\emptyset \subseteq\{a, b\}$
Hint: Empty set is an improper subset

Question 7.
If $A \cup B=A \cap B$, then
(1) $A \neq B$
(2) $A=B$
(3) $A \subset B$
(4) $\mathrm{B} \subset \mathrm{A}$
Solution:
(2) $A=B$

Question 8 .
If $B-A$ is $B$, then $A \cap B$ is
(1) $\mathrm{A}$
(2) $\mathrm{B}$
(3) $\mathrm{U}$
(4) $\varnothing$
Solution:
(4) $\varnothing$
Hint: $B-A=B \Rightarrow A$ and $B$ are disjoint sets.

Question $9 .$
From the adjacent diagram $n[\mathrm{P}(\mathrm{A} \Delta \mathrm{B})$ is
(1) 8
(2) 16
(3) 32
(4) 64

Solution:
$\begin{aligned}
&\text { (3) } 32 \\
&\operatorname{Hint:} A \Delta B=\{60,85,75,90,70\} \\
&\Rightarrow n(A \Delta B)=5 \\
&\Rightarrow n(P(A \Delta B))=2^{5}=32
\end{aligned}$
 

Question 10 .
If $n(A)=10$ and $n(B)=15$ then the minimum and maximum number of elements in $A$ $\cap \mathrm{B}$ is
(1) $(10,15)$
(2) $(15,10)$
(3) $(10,0)$
(4) $(0,10)$
Solution:
(4) $(0,10)$

Question 11 .
Let $A=\{\emptyset\}$ and $B=P(A)$ then $A \cap B$ is
(1) $\{\varnothing,\{\varnothing\}\}$
(2) $\{\emptyset\}$
(3) $\varnothing$
(4) $\{0\}$
Solution:
(2) $\{\varnothing\}$
Hint: $P(A)=\{\emptyset\{\emptyset\}\}$

Question $12 .$
In a class of 50 boys, 35 boys play carom and 20 boys play chess then the number of boys play both games is
(1) 5
(2) 30
(3) 15
(4) 10
Solution:
(1) 5
Hint: $n(A \cup B)=n(A)+n(B)-n(A n B) \Rightarrow 50=35+20-n(A \cap B) \Rightarrow n(A \cap B)=5$
 

Question $13 .$
If $U=\{x: x \in N$ and $x<10\}, A=\{1,2,3,5,8\}$ and $B=\{2,5,6,7,9\}$, then $n[(A \cup$ $\left.B)^{+}\right]$is
(1) 1
(2) 2
(3) 4
(4) 8
Solution:
(1) 1
Hint: $U=\{1,2,3,4,5,6,7,8,9\}$
$\mathrm{A}=\{1,2,3,5,8\}$
$\mathrm{B}=\{2,5,6,7,9\}$
$\mathrm{A} \cup \mathrm{B}=\{1,2,3,5,6,7,8,9\}$
$(A \cup B)^{\prime}=\{4\}$,
$\mathrm{n}(\mathrm{A} \cup \mathrm{B})^{\prime}=1$
 

Question $14 .$
For any three sets $P, Q$ and $R, P-(Q \cap R)$ is
(1), $P-(Q \cup R)$
(2) $(P \cap Q)-R$
(3) $(P-Q) \cup(P-R)$

(4) $(\mathrm{P}-\mathrm{Q}) \cap(\mathrm{P}-\mathrm{R})$
Solution:
(3) $(P-Q) \cup(P-R)$
Hint: $P-(Q \cap R)=(P-Q) \cup(P-R)$
 

Question $15 .$
Which of the following is true?
(1) $A-B=A \cap B$
(2) $\mathrm{A}-\mathrm{B}=\mathrm{B}-\mathrm{A}$
(3) $(A \cup B)^{\prime}=A^{\prime} \cup B^{\prime}$
(4) $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
Solution:
(4) $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
Hint: (1) $(A-B)=A \cap B X$
(2) $A-B=B-A X$
(3) $(A \cup B)=A^{\prime} \cup B^{\prime} X$
(4) $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \checkmark$
 

Question $16 .$
If $n(A \cup B \cup C)=100, n(A)=4 x, n(B)=6 x, n(C)=5 x, n(A \cap B)=20, n(B \cap C)=15$, $n(A \cap C)=25$ and $n(A \cap B \cap C)=10$, then the value of $x$ is
(A) 10
(B) 15
(C) 25
(D) 30
Solution:
(A) 10
Hint:
$n(A \cup B \cup C)=n(A)+n(B)+n(C)-n(A \cap B)-n(B \cap C)-n(C \cap A)+n(A \cap B \cap$C)
$100=4 x+6 x+5 x-20-15-25+10$
$100=15 x-60+10$
$100=15 x-50$
$\therefore 15 x=100+50=150$

$x=10$
 

Question 17.
For any three sets $A, B$ and $C,(A-B) \cap(B-C)$ is equal to
(1) A only
(2) B only
(3) Conly
(4) $\phi$
Solution:
(4) $\phi$
Hint: $(A-B) \cap(B-C)$ is equal to $\Phi$
 

Question $18 .$
If $\mathrm{J}=$ Set of three sided shapes, $\mathrm{K}=$ Set of shapes with two equal sides and $\mathrm{L}=$ Set of shapes with right angle, then $J \cap K \cap L$ is
(1) Set of isoceles triangles
(2) Set of equilateral triangles
(3) Set of isoceles right triangles
(4) Set of right angled triangles
Solution:
(3) Set of isoceles right triangles

Question $19 .$
The shaded region in the Venn diagram is
(1) $Z-(X \cup Y)$
(2) $(X \cup Y) \cap Z$
(3) $Z-(X \cap Y)$
(4) $Z \cup(X \cap Y)$
Answer:
(3) $Z-(X \cap Y)$

Question 20 .
In a city, $40 \%$ people like only one fruit, $35 \%$ people like only two fruits, $20 \%$ people like all the three fruits. How many percentage of people do not like any one of the above three fruits?
(1) 5
(2) 8
(3) 10
(4) 15
Answer:
(1) 5