Question 11 Mark
State the sets representing by the shaded portion of following venn$-$diagram :
Answer
View full question & answer→$(B - A)'$
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Question 21 Mark
State the sets representing by the shaded portion of following venn$-$diagram :
Answer
View full question & answer→$B - A$ or $A' ∩ B$
Question 31 Mark
State the sets representing by the shaded portion of following venn$-$diagram :
Answer
View full question & answer→$(A ∪ B)'$
Question 41 Mark
Use the given Venn$-$diagram to find $:A ∪ B$
Answer
View full question & answer→$A ∪ B = \{1, 5, 6, 7, 9\} ∪ \{1,5\}$
$= \{1,5, 6, 7, 9\}$
$= \{1,5, 6, 7, 9\}$
Question 51 Mark
Use the given Venn$-$diagram to find$ \ :A ∩ B$
Answer
View full question & answer→$A ∩ B = \{1, 5, 6, 7, 9\} ∩ \{1,5\}$
$= \{1,5\}$
$= \{1,5\}$
Question 61 Mark
Use the given Venn$-$diagram to find $: B'$
Answer
View full question & answer→$B = \{1, 5\}$
$∴ B' = \{2, 3, 4, 6, 7, 8, 9, 10\}$
$∴ B' = \{2, 3, 4, 6, 7, 8, 9, 10\}$
Question 71 Mark
Use the given Venn$-$diagram to find $ :\ A$
Answer
View full question & answer→$A = \{1, 5, 6, 7, 9\}$
Question 81 Mark
Use the given Venn$-$diagram to find $:\ B - A$
Answer
View full question & answer→$B - A = \{1, 5\} - \{1, 5, 6, 7, 9\}$
$= \{ \}$
$= \{ \}$
Question 91 Mark
From the given diagram find$ :(A ∪ B)'$
Answer
View full question & answer→$A ∪ B = \{a, b, c, d, e, f\}$
$∴ (A ∪ B)' = \{h, g\}$
$∴ (A ∪ B)' = \{h, g\}$
Question 101 Mark
From the given diagram find $:B - A$
Answer
View full question & answer→$B - A = \{b, c, e, f\} - \{a, c, d, e\}$
$= \{b, f\}$
$= \{b, f\}$
Question 111 Mark
From the given diagram find$ :A - B$
Answer
View full question & answer→$A - B = \{a, c, d, e\} - \{b, c, e, f\}$
$⇒ A - B = \{a, d\}$
$⇒ A - B = \{a, d\}$
Question 121 Mark
From the given diagram find $:A' ∩ B$
Answer
View full question & answer→$A' = \{b ,f, g, h\}$
$A' ∩ B =\{b, f, g, h\} ∩\{b, c, e, f\}$
$⇒ A' ∩ B = \{b, f\}$
$A' ∩ B =\{b, f, g, h\} ∩\{b, c, e, f\}$
$⇒ A' ∩ B = \{b, f\}$
Question 131 Mark
From the given diagram find $:A ∪ B$
Answer
View full question & answer→$A ∪ B =\{a, c, d, e\} ∪ \{b, c, e, f\}$
$⇒ A ∪ B = \{a, b, c, d, e, f\}$
$⇒ A ∪ B = \{a, b, c, d, e, f\}$
Question 141 Mark
Using the given diagram, express the following sets in the terms of $A$ and $B. \ \{g, h\}$
Answer
View full question & answer→$\{g, h\} = (A ∪ B)'$
$[\because A ∪ B = \{a, b, c, d, e, f\} \therefore (A ∪ B)' = \{g, h\}]$
$[\because A ∪ B = \{a, b, c, d, e, f\} \therefore (A ∪ B)' = \{g, h\}]$
Question 151 Mark
Using the given diagram, express the following sets in the terms of $A $and $B.\ \{a, d, g, h\}$
Answer
View full question & answer→$\{a, d, g, h\} = B'$
$[\because \{b, c, e, f\} = B \therefore B' =\{a, d, g, h\}]$
$[\because \{b, c, e, f\} = B \therefore B' =\{a, d, g, h\}]$
Question 161 Mark
Using the given diagram, express the following sets in the terms of $A$ and $B.\{a, d, c, f, g, h\}$
Answer
View full question & answer→$\{a, d, c, f, g, h\} = (A ∩ B)'$
$[\because \{b, e\} = A ∩ B \therefore (A ∩ B)' = \{a, d, c, f, g, h\}]$
$[\because \{b, e\} = A ∩ B \therefore (A ∩ B)' = \{a, d, c, f, g, h\}]$
Question 171 Mark
Using the given diagram, express the following sets in the terms of $A$ and $B . \{a, d\}$
Answer
View full question & answer→$\{a, d\} =\{a, b, e, d\} - \{b, c, e, f\}$
$= A - B$
$= A - B$
Question 181 Mark
$If P =\{x : x ∈ W $and $ 4 ≤ x ≤ 8\}, $and $Q =\{x : x ∈ N $ and $ x < 6\}.$ Find: $Is (P ∪ Q) ⊃ (P ∩ Q)?$
Answer
View full question & answer→Yes, all the element of set $P ∪ Q$ are contained in the set $P ∩ Q.$ Therefore $P ∪ Q $ is a proper subset of $P ∪ Q$.
Question 191 Mark
Given $A = \{x : x \in N \ $and $\ 3 < x \sim 6\} $and $8 =\{x : x \in W $ and $ x < 4\}. $ Find $: B - A.$
Answer
View full question & answer→$B - A = (0, 1, 2, 3)$
Question 201 Mark
Given $A =\{x : x \in N$ and $3 < x \sim 6\}$ and $8 =\{x : x \in W$ and $x < 4\}.$ Find:$ A - B.$
Answer
View full question & answer→$A - B = (4, 5, 6)$
Question 211 Mark
Given $A = \{x : x \in N$ and $3 < x \sim 6\}$ and $8 = \{x : x \in W$ and $x < 4\}$. Find: $A ∩ B.$
Answer
View full question & answer→$A ∩ B = ( \Phi )$
Question 221 Mark
Given $A = \{x : x \in N$ and $3 < x \sim 6\} $ and $ 8 = \{x : x\ \in W$ and $x < 4\}$. Find:$ A ∪ B$
Answer
View full question & answer→$A ∪ B = \{0, 1, 2, 3, 4, 5, 6\}$
Question 231 Mark
Given $A = \{x : x \in N$ and $3 < x \leq 6\}$ and $B = \{x : x \in W$ and $x < 4\}$. Find : Sets $A$ and $B$ in roster form.
Answer
View full question & answer→$A = (4, 5, 6)$
$B = (0, 1 2, 3)$
$B = (0, 1 2, 3)$
Question 241 Mark
Given the universal set $=\{-7,-3, -1, 0, 5, 6, 8, 9\},$ find: $B =\{x : -4 < x < 6\}$
Answer
View full question & answer→$Universal set = \{-7, -3, -1, 0, 5, 6, 8, 9\},$
$B = \{x : -4 < x < 6\} = \{-3, -1, 0, 5\}$
$B = \{x : -4 < x < 6\} = \{-3, -1, 0, 5\}$
Question 251 Mark
Given the universal set $= \{-7,-3, -1, 0, 5, 6, 8, 9\}, $find: $A = \{x : x < 2\}$
Answer
View full question & answer→Universal set = {-7, -3, -1, 0, 5, 6, 8, 9},
A = {x : x < 2} = {-7, -3, -1, 0}
A = {x : x < 2} = {-7, -3, -1, 0}
Question 261 Mark
$If T =\{x : x $ is a letter in the word ‘$\text{TEETH’\}}$, find all its subsets.
Answer
View full question & answer→$T = \{t,e,h\}$
Subsets of set $T = φ, \{r\}, \{e\}, \{h\}, \{t,e\}, \{t,h\}, \{e,h\}, \{t,e,h\}$
Subsets of set $T = φ, \{r\}, \{e\}, \{h\}, \{t,e\}, \{t,h\}, \{e,h\}, \{t,e,h\}$
Question 271 Mark
If $C$ is the set of letters in the word “$\text{cooler”}$, find: Number of its proper subsets.
Answer
View full question & answer→Number of its proper subsets $=2^5-1=32-1=31$
Question 281 Mark
If $C$ is the set of letters in the word $\text{“cooler”}$, find: The number of its subsets.
Answer
View full question & answer→Number of its subsets: $2^5=2 \times 2 \times 2 \times 2 \times 2=32$
Question 291 Mark
If $C$ is the set of letters in the word $\text{“cooler”},$ find $: n(C)$
Answer
View full question & answer→$n(C) = 5$
Question 301 Mark
If $C$ is the set of letters in the word $\text{“cooler”}$, find : Set $C$
Answer
View full question & answer→$C = \{c, o, l, e, r\}$
Question 311 Mark
Find the subset of the following set:{$p : p$ is a letter in the word $‘poor$’}
Answer
View full question & answer→$\{P : P $ is a letter in the word $‘\text{POOR’}\}$
$= \{p, o, o, r\}$
∴ Subsets of the given set $= Φ,\{p\},\{o\},\{r\}, \{p,o\},\{p,r\},\{p,r\}, \{o,r\}, \{p,o,r\}$
$= \{p, o, o, r\}$
∴ Subsets of the given set $= Φ,\{p\},\{o\},\{r\}, \{p,o\},\{p,r\},\{p,r\}, \{o,r\}, \{p,o,r\}$
Question 321 Mark
Find the subset of the following set: $C =\{x : x ∈ W, x ≤ 2\}$
Answer
View full question & answer→$C = \{x : x ∈ W, x ≤ 2\}$
= $\{0, 12\}$
$∴ Subsets of set C = Φ, \{0\}, \{1\}, \{2\}, \{0,1\}, \{0,2\}, \{1,2\}, \{0,1,2\}$
= $\{0, 12\}$
$∴ Subsets of set C = Φ, \{0\}, \{1\}, \{2\}, \{0,1\}, \{0,2\}, \{1,2\}, \{0,1,2\}$
Question 331 Mark
Find the subset of the following set $:B=\{a, b, c\}$
Answer
View full question & answer→$B = \{a, b, c\}$
Subsets of set $B = \{\}, \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}.$
Subsets of set $B = \{\}, \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}.$
Question 341 Mark
Find the subset of the following set$:$ $A = \{5, 7\}$
Answer
View full question & answer→$A = \{5,7\}$
$Subsets of set A =\{ \},\{5\},\{7\},\{5,7\}$
$Subsets of set A =\{ \},\{5\},\{7\},\{5,7\}$
Question 351 Mark
State if the following set is a finite set or an infinite set:$\left\{x: x=\frac{n-2}{n+2}, n \in w \right)$
Answer
View full question & answer→$\left\{x: x=\frac{n-2}{n+2}, n \in w \right)$
$\left\{-2,-\frac{1}{2}, 0, \frac{1}{4}, \frac{2}{5} \ldots \ldots\right\}$
It is infinite set.
$\left\{-2,-\frac{1}{2}, 0, \frac{1}{4}, \frac{2}{5} \ldots \ldots\right\}$
It is infinite set.
Question 361 Mark
State if the following set is a finite set or an infinite set $:\{x : x = 3n – 2,n ∈ Z, n ≤ 8\}$
Answer
View full question & answer→$\{x : x = 3n – 2,n ∈ Z, n ≤ 8\}$
$= \{22, 19, 16, 13, 10, 7, 4, 1, -2, -5, ....\}$
It is infinite set.
$= \{22, 19, 16, 13, 10, 7, 4, 1, -2, -5, ....\}$
It is infinite set.
Question 371 Mark
State if the following set is a finite set or an infinite set : The set of whole numbers less than $12.$
Answer
View full question & answer→$The set of whole numbers less than 12$
$= \{11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0\}$
>$\ It\ is\ a\ finite\ set.$
$= \{11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0\}$
>$\ It\ is\ a\ finite\ set.$
Question 381 Mark
State if the following set is a finite set or an infinite set:The set of integers less than $10.$
Answer
View full question & answer→The set of integers less than $10$.
=$ \{ 9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -1, -2, .....\}$
It is an infinite set.
=$ \{ 9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -1, -2, .....\}$
It is an infinite set.
Question 391 Mark
State if the following set is a finite set or an infinite set $:$ The set of multiples of $8.$
Answer
View full question & answer→The set of multiples of $8.$
$= \{8, 16, 24, 32, .....\}$
It is an infinite set.
$= \{8, 16, 24, 32, .....\}$
It is an infinite set.
Question 401 Mark
Find, if the following sets are empty : $D = \{$prime numbers between $7 \&11\}$
Answer
View full question & answer→$D$ ={Prime numbers between $7 \&11\}$
Because there is no prime number between $7$ and $11$.<
$∴ D = \{ \}$
Hence it is an empty set.
Because there is no prime number between $7$ and $11$.<
$∴ D = \{ \}$
Hence it is an empty set.
Question 411 Mark
Find, if the following sets are empty : $C $={even numbers between $6 \& 10\}$
Answer
View full question & answer→$C $= {Even numbers between $6\&10\}$
$∴ C =\{8\}$
Hence it is not an empty set.
$∴ C =\{8\}$
Hence it is not an empty set.
Question 421 Mark
Find$, $if the following sets are empty $:$ The set of points of intersection of two parallel lines.
Answer
View full question & answer→$"$The set of points of intersection of two parallel lines$"$ is an empty set because two parallel lines do not intersect anywhere.
Question 431 Mark
Find$,$ if the following sets are singleton sets $:$ The set of points of intersection of two non-parallel st. lines in the same plane
Answer
View full question & answer→The set of points of intersection of two non-parallel st. lines in the same plane$......$singleton set.
Question 441 Mark
$If P = \{P : P$ is a letter in the word $\text{“PERMANENT”}$}. Find $n (P)$.
Answer
View full question & answer→$P = (P : P$ is a letter in the word $\text{“PERMANENT”}$}
or $ P$ =$ \{p, e, r, m, a, n, t\}$
$n (P) = 7$
or $ P$ =$ \{p, e, r, m, a, n, t\}$
$n (P) = 7$
Question 451 Mark
Find the cardinal number of the following sets $:A_1 = {-2, -1, 1, 3, 5}$
Answer
View full question & answer→$A_1 = {-2, -1, 1, 3, 5}$
Cardinal number of set $A_1 = 5$
Cardinal number of set $A_1 = 5$
Question 461 Mark
Write the following sets in Roster form $:$ The set of letters in the word $\text{‘UNIVERSAL}’.$
Answer
View full question & answer→Roster form of the set of letters in the word$\text{ “UNIVERSAL”} =\{u, n, i, v, e, r, s, a, l\}$
Question 471 Mark
Write the following sets in Roster form $:$ The set of letters in the word $\text{ ‘MEERUT’}$
Answer
View full question & answer→Roster form of the set of letters in the word $\text"{“MEERUT”}$ $= \{m, e, r, u, t\}$
Question 481 Mark
Is $\{x : x$ is a factor of $27\} \neq \{3, 9, 27, 54\} ?$ Give reason.
Answer
View full question & answer→Yes ,$\{x : x$ is a factor of $27\} +\{3, 9, 27, 54\}$
Because $54$ is not a factor of $27$
Because $54$ is not a factor of $27$
Question 491 Mark
Is $\{1, 2, 4, 16, 64\}$ = $\{x : x $is a factor of $32\}?$ Give reason.
Answer
View full question & answer→No$, {1, 2, 4, 16, 64}$ ≠ $\{x : x$ is factor of $32\}$
Because $64$ is not a factor of $ 32$
Because $64$ is not a factor of $ 32$
Question 501 Mark
Write the following sets in set-builder$ (Rule Method) $form : $B_6 = {....., -6, -3, 0, 3, 6 ......}$
Answer
View full question & answer→$B_6 = \{....., -6, -3, 0, 3, 6, ......\}$
$= \{x : x = 3n, n \in Z\}$
$= \{x : x = 3n, n \in Z\}$