(Each question 1 marks)

Question 11 Mark

Using properties of sets, show that: $A \cap (A \cup B) = A$

Answer

We know that if $A \subset B$then
$A \cap B = A$
Also$A \subset A \cup B$
$\therefore A \cap (A \cup B) = A$

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Question 21 Mark

Using properties of set, show that:$A \cup (A \cap B) = A$

Answer

We know that if $A \subset B$then
$A \cap B = B$
Also $A \cap B \subset A$
$\therefore A \cup (A \cap B) = A$

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Question 31 Mark

Show that for any sets A and B, A = ( A $\cap$B ) $\cup$( A – B ) and A $\cup$( B – A ) = ( A $\cup$B )

Answer

We have to prove: $A=(A \cap B) \cup(A-B)$
Proof: Let $x \in A$
Now, we need to show that $x \in(A \cap B) \cup(A-B)$
In Case I,
$x \in(A \cap B)$
$\Rightarrow X \in(A \cap B) \subset(A \cup B) \cup(A-B)$
In Case II,
$X \notin A \cap B$
$\Rightarrow x \notin B \ or \ x \notin A$
$\Rightarrow X \notin B(X \notin A)$
$\Rightarrow X \notin A-B \subset(A \cup B) \cup(A-B)$
$\therefore A \subset(A \cap B) \cup(A-B)(i)$
It can be concluded that, $A \cap B \subset A \ and \ (A-B) \subset A$
Therefore, (A $\cap$B) $\cap$(A - B) $\subset $A (ii)
Equating (i) and (ii),we get
$A=(A \cap B) \cup(A-B)$
Now, we need to show, $A \cup(B-A) \subset A \cup B$
Suppose that,
$X \in A \cup(B-A)$
$X \in A \ or \ X \in(B-A)$
$\Rightarrow X \in A \ or \ (X \in B \text { and } X \notin A)$
$\Rightarrow(X \in A \text { or } X \in B) \ and \ (X \in A \text { and } X \notin A)$
$\Rightarrow X \in(B \cup A)$
$\therefore A \cup(B-A) \subset(A \cup B)$(iii)
Now, to prove: $(A \cup B) \subset A \cup(B-A)$
Let y $\in A\cup B$
$\mathrm{y} \in \mathrm{A}\ or \ \mathrm{y} \in \mathrm{B}$
$(y \in A \text { or } y \in B)\ and \ (X \in A \text { and } X \notin A)$
$\Rightarrow y \in A \ or \ (y \in B \text { and } y \notin A)$
$\Rightarrow y \in A \cup(B-A)$
Therefore,$A \cup B \subset A \cup(B-A)$(iv)
$\therefore$ Using (iii) and (iv), we obtain
$A \cup(B-A)=A \cup B$

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Question 41 Mark

Is it true that for any sets A and B,$P(A) \cup P(B) = P(A \cup B)?$Justify your answer.

Answer

No, it is not true.
Take A = {1, 2} ad B = {2, 3}
Then$A \cup B = \{ 1,2,3\} $
$P(A) = \{ \phi ,\{ 1\} ,\{ 2\} ,\{ 1,2\} \}$
$P(B) = \{ \phi ,\{ 2\} ,\{ 3\} ,\{ 2,3\} \}$
$\therefore P(A) \cup P(B) = \{ \phi ,\{ 1\} ,\{ 2\} ,\{ 3\} ,\{ 1,2\} ,\{ 2,3\} \} $. . (i)
$A \cup B = \{ 1,2,3\}$

$P(A \cup B) = \{ \phi \}$,{1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}} . . . (ii)
From (i) and (ii), we have
$P(A \cup B) \ne P(A) \cup P(B)$

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Question 51 Mark

Assume that P(A) = P(B) show that A = B.

Answer

Let$X \in A \Rightarrow \{ x\} \in P(A)$
$\Rightarrow \{ x\} \in P(B)\,[\because P(A) = P(B)]$
$\Rightarrow X \notin B$
$\therefore A \subset B$. . . (i)
Let $X \in B \Rightarrow \{ x\} \in P(B)$
$\Rightarrow \{ X\} \in P(A)\,[\because \,P(A) = P(B)]$
$ \Rightarrow X \in A$. . . (ii)
$\therefore B \subset A$
From (i) and (ii) we have A = B

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Question 61 Mark

Show that if $A \subset B$then$C - B \subset C - A.$

Answer

Let$x \in C - B \Rightarrow x \in C$and $x \notin B$
$\Rightarrow x \in C$and$x \notin A$$[\because A \subset B]$
$\Rightarrow x \in C - A$Hence$C - B \subset C - A.$

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Question 71 Mark

Let A, B and C be the sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$ Show that B = C.

Answer

We know that$A = A \cap (A \cup B)$and$A = A \cup (A \cap B)$
Now $A \cap B = A \cap C$and$A \cup B = A \cup C$
$\therefore B = B \cup (B \cap A) = B \cup (A \cap B) = B \cup (A \cap C)$$[\because \,A \cap B = A \cap C]$
$ = (B \cup A) \cap (B \cup C)$(By distributive law)
$ = (A \cup C) \cap (B \cup C)$
$ = (A \cup C) \cap (B \cup C)$$[\because \,A \cup B = A \cup C]$
$ = (C \cup A) \cap (C \cup B)$
$= C \cup (A \cap B)$(by distributive law)
$ = C \cup (A \cap C)$$[\because \,A \cap B = A \cap C]$
$ = C \cup (C \cap A) = C$
Hence B = C.

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Question 81 Mark

If A $\subset$ B and x $\notin$ B, then x $\notin$A.If it is true, prove it. If it is false, give an example.

Answer

It is given in the question that,
$A \subset B$
Andx $\notin$ B
Let us suppose, $\mathrm{x} \in \mathrm{A}$ then we have:
$\mathbf{x} \in \mathbf{B}$
But it is given in the question that, $x \notin B$
$\therefore \ x \notin A$
Hence, the given statement is true.

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Question 91 Mark

If x $\in$ A and A $\not \subset$B , then x $\in$B.If it is true, prove it. If it is false, give an example.

Answer

It is given in the question that,
x $\in$ A
And, A$\not \subset$B
Let us now assume, A = {3, 5, 7}
And, B = {3, 4, 6}
As, 5$\in$ A
And,A$\not \subset$B
$\therefore$5$\notin$B
Hence, the given statement is false

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Question 101 Mark

If $A \not \subset B$ and $B \not \subset C$ , then $A \not \subset C$.If it is true, prove it. If it is false, give an example.

Answer

It is given in the question that,
$A \not \subset B$
And$B \not \subset C$
Let us now assume, A = {1, 2}
B = {0, 6, 8}
And, C = {0, 1, 2, 6, 9}
$\therefore $A $\subset$ C
Hence, the given statement is false

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Question 111 Mark

If A $\subset$ B and B $\subset$C , then A $\subset$C.If it is true, prove it. If it is false, give an example.

Answer

It is given in the question that, $A \subset B \ and \ B \subset C$
Let us assume, $x \in A$
So, $x \in B$
And $x \in C$
$\therefore$ A $\subset$ C
Hence, the given statement is True

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Question 121 Mark

If A $\subset$ B and B $\in$ C , then A $\in$C.If it is true, prove it. If it is false, give an example.

Answer

Let us assume, A {2}
B = {0, 2}
And, C = {1, {0, 2}, 3}
It is given in the question that,
$A \subset B$
$\therefore \ B \in C$
But, $A \notin C$
Hence, the given statement is false

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Question 131 Mark

If x $\in$A and A $\in$B , then x $\in$B.If it is true, prove it. If it is false, give an example.

Answer

Let us assume A = {1, 2}
And, B = {1, {1, 2},{3}}
So, 2$\in$ {1, 2}
And,{1, 2}$\in${{3}, 1, {1, 2}}
$\therefore$ A $\in$B
But, 2 $\notin${{3}, 1, {1,2}}
Hence, the given statement is false

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Question 141 Mark

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read exactly one newspaper.

Answer

Here
n(U) = a + b + c + d + e + f + g + h = 60 ....(i)
n(H) = a + b + c +d = 25 ....(ii)
n(T) = b + c + f + g = 26 .....(iii)
n(I) = c + d + e + f = 26 ....(iv)
$n(H \cap I) $ = c + d = 9 ....(v)
$n(H \cap T) $= b + c = 11 .....(vi)
$n(T \cap I) $ = c + f = 8 .....(vii)
$n(H \cap T \cap I) $ = c = 3 ....(viii)

Putting value of c in (vii),
3 + f = 8 $\Rightarrow$ f = 5
Putting value of c in (vi),
3 + b = 11 $\Rightarrow$ b = 8
Putting values of c in (v),
3 + d = 9 $\Rightarrow$ d = 6
Putting value of c, d, f in (iv),
3 + 6 + e + 5 = 26 $\Rightarrow$ e = 26 - 14= 12
Putting value of b, c, f in (iii),
8 + 3 + 5 + g = 26 $\Rightarrow$ g = 26 - 16= 10
Putting value of b, c, d in (ii)
a + 8 + 3 + 6 = 25 $\Rightarrow$ a = 25 - 17 = 8
Number of people who read exactly one newspapers
= a + e + g
= 8 + 12 + 10 = 30

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Question 151 Mark

Answer

Here
n(U) = a + b + c + d + e + f + g + h = 60....(i)
n (H) = a + b + c +d = 25....(ii)
n(T) = b + c + f + g = 26 .....(iii)
n(I) = c + d + e + f = 26....(iv)
$n(H \cap I) $ = c + d = 9 .....(v)
$n(H \cap T) $ = b + c = 11 .....(vi)
$n(T \cap I) $= c + f = 8 ....(vii)
$n(H \cap T \cap I) $= c = 3 ....(viii)

Putting value of c in (vii),
3 + f = 8 $\Rightarrow$f = 5
Putting value of c in (vi),
3 + b = 11$\Rightarrow$b = 8
Putting values of c in (v),
3 + d = 9$\Rightarrow$d = 6
Putting value of c, d, f in (iv),
3 + 6 + e + 5 = 26$\Rightarrow$ e = 26 - 14= 12
Putting value of b, c, f in (iii),
8 + 3 + 5 + g = 26 $\Rightarrow$g = 26 - 16= 10
Putting value of b, c, d in (ii)
a + 8 + 3 + 6 = 25 $\Rightarrow$a = 25 - 17 = 8
Number of people who read at least one of the three newspapers
= a + b + c + d + e + f + g
= 8 + 8 + 3 + 6 + 12 + 5 + 10 = 52

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Question 161 Mark

In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Answer

Let H be the set of students who know Hindi and E be the set of students who know English.
Here n(H) = 100, n(E) = 50 and$n(H \cap E) = 25$
We know that$n(H \cup E) = n(H) + n(E) - n(H \cap E)$
= 100 + 50 - 25 = 125.

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Question 171 Mark

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee.

Answer

Let T be the set of students who like tea and C be the set of students who like coffee.
Here n(T) = 150, m (C) = 225 and$n(C \cap T) = 100$
We know that$n(C \cup T) = n(C) + n(T) - n(C \cap T)$
= 150 + 225 - 100 = 275
$\therefore$Number of students taking either tea or coffee += 275
$\therefore$Number of students taking neither tea nor coffee = 600 - 275 = 325

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Question 181 Mark

If $A \not \subset B$ and $B \not \subset C$ , then $A \not \subset C$.If it is true, prove it. If it is false, give an example.

Answer

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Question 191 Mark

Find sets A, B and C such that$A \cap B,B \cap C$and $A \cap C$are non-empty sets and$A \cap B \cap C = \phi $

Answer

Take A = {1, 2} B = {1, 4} and C = {2, 4}
Now$A \cap B = \{ 1\} \ne \phi$
$B \cap C = \{ 4\} \ne \phi$
$A \cap C = \{ 2\} \ne \phi$
But$A \cap B \cap C = \phi$

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Question 201 Mark

Show that $A \cap B = A \cap C$need not imply B = C.

Answer

Let A = {1, 2, 3, 4} , B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
$\therefore A \cap B$= {1, 2, 3, 4} $ \cap ${2, 3, 4, 5, 6}
= {2,3, 4}
$A \cap C$= {1, 2, 3, 4}, B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
= {2, 3, 4}
$A \cap C$= {1, 2, 3, 4} $ \cap ${2, 3, 4, 9, 10}
= {2, 3, 4}
Now we have$A \cap B = A \cap C$
But$B \ne C$

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Question 211 Mark

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Answer

Let F be the set of people who speak French and 'S' be the set of people who speak Spanish.
Here n(F) = 50, n(S) = 20 and $n(F \cap S) = 10$
We know that$n(F \cup S) = n(F) + n(S) - n(F \cap S)$
$\therefore n(F \cup S) = 50 + 20 - 10 = 60$
Number of people who speak at least one of these two languages = 60

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Question 221 Mark

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Answer

Let C be the set of people who like cricket and T be the set of people who like tennis.
Here n(C) = 40,$n(C \cap T) = 10$and $n(C \cup T) = 65$
We know that$n(C \cup T) = n(C) + n(T) - n(C \cap T)$
$\therefore$65 = 40 + n(T) - 10
$\therefore$n(T) = 65 - 30= 35
Number of people who like tennis = 35
Now number of people who like tennis only and not cricket
= n(T - C)

$ = n(T) - n(C \cap T)$
= 35 - 10 = 25

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Question 231 Mark

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Answer

Let C be the set of persons who like coffee and T be the set of persons who like tea.
$\therefore $n(C) = 30,n(T) = 52 and$n(C \cup T) $ = 70
We know that$n(C \cup T) = n(C) + n(T) - n(C \cap T)$
$\therefore$ 70 = 37 + 52 - n(C$ \cap$ T)
$\therefore n(C \cap T) $ = 89 - 70 = 19

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Question 241 Mark

If X and Y are two sets such that X has 40 elements$X \cup Y$has 60 elements and$X \cap Y$has 10 elements, how many elements does Y have?

Answer

Here n(X) = 40,$n(X \cup Y) = 60$and$n(X \cap Y) = 10$
We know that$n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)$
60 = 40 + n(Y) - 10
$\therefore n(Y) = 60 - 30 = 30.$

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Question 251 Mark

If S and T are two sets such that S has 21 elements T has 32 elements and$S \cap T$has 11 elements, how many elements does$S \cup T$have?

Answer

Here n(S) = 21, n(T) = 32 and$n(S \cap T) = 11$

We know that$n(S \cup T) = n(S) + n(T) - n(S \cap T)$

$\therefore n(S \cup T) = 21 + 32 - 11 = 42.$

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Question 261 Mark

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English.

Answer

Let H be the set of people speaking Hindi and E be the set of people speaking English.
$\therefore$n(H) = 250, n(E) = 200 and $n(H \cup E) = 400$
We have to find $n(H \cap E)$
We know that$n(H \cap E) = n(H) + n(E) - n(H \cap E)$
$\therefore 400 = 250 + 200 - n(H \cap E)$
$\therefore n(H \cap E) = 450 - 400 = 50$

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Question 271 Mark

If X and Y are two sets such that X $\cup$Y has 18 elements, X has 8 elements and Y has 15 elements ; how many elements does X $\cap$Y have?

Answer

Here,
n(X) = 8, n(Y) = 15, and n(X$\cup$ Y) = 18
We know that-
n(X$\cup$ Y) = n(X) + n(Y) -n(X$\cap$ Y)
$\Rightarrow$18 = 8 + 15-n(X$\cap$ Y)
$\Rightarrow$18 = 23-n(X$\cap$ Y)
$\Rightarrow$n(X$\cap$ Y) = 23 - 18

Therefore,
$$ n(X$\cap$ Y) = 5

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Question 281 Mark

If X andY are two sets such that n(X) = 17, n(Y) = 23 and n ( X $\cup$ Y) = 38, find n(X $\cap$ Y).

Answer

We know that,
$n ( X \cup Y ) = n ( X ) + n ( Y ) - n ( X \cap Y )$
$\Rightarrow 38 = 17 + 23 - n ( X \cap Y )$
$\Rightarrow n ( X \cap Y )$ = 40 - 38 = 2

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Question 291 Mark

U′ $\cap$ A = ________

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Question 301 Mark

A $\cap$ A′ = ________

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Question 311 Mark

$\phi$′ $\cap$ A = ________

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Question 321 Mark

A $\cup$ A′ = ________

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Question 331 Mark

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60° what is ${A'}$?

Answer

Here U = {x : x is a triangle}
A = {x : x is a triangle and has at least one angle different from 60°}
$\therefore A' = U - A = ${x : x is a triangle} - {x : x is a triangle and has atleast one angle different from 60°}
= {x : x is a triangle and has all angles equal to 60°}
= Set of all equilateral triangles.

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Question 341 Mark

Draw appropriate Venn diagram for: A'$\cup$ B'

Answer

The Venn diagram for A'$\cup$ B' The shaded portion represents A'$\cup$ B'

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Question 351 Mark

Draw appropriate Venn diagram for: $(A \cap B)'$

Answer

The Venn diagram for$(A \cap B)'$The shaded portion represents$(A \cap B)'$

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Question 361 Mark

Draw appropriate Venn diagram for: A' $\cap$B'

Answer

The Venn diagram forA' $\cap$B' The shaded portion representsA' $\cap$B'

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Question 371 Mark

Draw appropriate Venn diagram for:$(A \cup B)'$

Answer

The Venn diagram for$(A \cup B)'$The shaded portion represents $(A \cup B)'$

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Question 381 Mark

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cap$ B)' = A' $\cup$ B'.

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
$A \cap B $ = {2, 4, 6, 8} $\cap$ {2, 3, 5, 7}
= {2}
$(A \cap B)' = U - (A \cap B) $ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2}
= {1, 3, 4, 5, 6, 7, 8, 9} . . . (i)
A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 8}
B' = U - B = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}
= {1, 4, 6, 8, 9}
$A' \cup B'$ = {1, 3, 5, 7, 9} $\cup$ {1, 4, 6, 8, 9}
= {1, 3, 4, 5, 6, 7, 8, 9} . . . (ii)
From (i) and (ii) we have
$(A \cap B)' = A' \cup B'$

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Question 391 Mark

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cup$ B)' = A' $\cap$ B'

Answer

Here U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
$A \cup B $ = {2, 4, 6, 8} $\cup$ {2, 3, 5, 7}
= {2, 3, 4, 5, 6, 7,8}
$\therefore (A \cup B)' = U - (A \cup B)$= {1,2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 4, 5, 6, 7, 8}
= {1, 9} . . . (i)
A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 9}
B' = U - B = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}
= {1, 4, 6, 8, 9}
$A' \cap B' $ = {1, 3, 5, 7, 9} $\cap$ {1, 4, 6, 8, 9} = {1, 9} ....(ii)
From (i) and (ii), we have
$(A \cup B)' = A' \cap B'$

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Question 401 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : 2x + 5 = 9}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : 2x + 5 = 9{ = {2}
$A' = U - A = \{ x:x \in N\} - \{ 2\}$
$= \{ x:x \in N,x \ne 2\}$

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Question 411 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x + 5 = 8}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x + 5 = 8} = {3}
$A' = U - A = \{ x:x \in N\} -$
$= \{ x:x \in N,x \ne 3\}$

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Question 421 Mark

Taking the set of natural numbesrs as the universal set, write down the complement of the set: {x : x is a perfect cube}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x is a perfect cube}
$A' = U - A = \{ x:x \in N\} -${x : x is a perfect cube}
= {x : x $ \in $N , x is not a perfect cube}

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Question 431 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a perfect square}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x is a perfect square}
$A' = U - A = \{ x:x \in N\} -${x : x is a perfect square}
= {$x:x \in N$, x is not a perfect square}

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Question 441 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a natural number divisible by 3 and 5}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x is a natural number divisible by 3 and 5}
$A' = U - A = \{ x:x \in N\} -${x : x is a natural number divisible by 3 and 5}
= {$x:x \in N$} - {x : x is a natural number divisible by 15}
= { $x:x \in N$, x is not divisible by 15}

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Question 451 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a prime number}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x is a prime number}
$A' = U - A = \{ x:x \in N\} -${x : x is a prime number}
= { $x:x \in N$, x is not a prime number}
or {x : x is positive composite number and x = 1}

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Question 461 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a positive multiple of 3}

Answer

Here $U = \{ x:x \in N\}$
Let A = {x : x is a positive multiple of 3}
$\therefore A' = U - A = \{ x:x \in N\} -${x :x is a positive multiple of 3}
= { $x:x \in N$, x is not a multiple of 3}

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Question 471 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set:{x : x is an odd natural number}

Answer

Here$U = \{ x:x \in N\}$

Let A = {x : x is an odd natural number}
$A' = U - A = \{ x:x \in N\} -${x : x is an odd natural number}
= {x : x is an even natural number}

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Question 481 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set:$\{ x:x \in N\,\,and\,\,2x + 1 > 10\}$

Answer

Here $U = \{ x:x \in N\}$
Let A = {$x:x \in N$and 2x + 1 > 10} = {5, 6, 7, 8 , . . . }
$A' = U - A = \{ x:x \in N\} - \{ 5,6,7,8,.....\}$
= {1, 2, 3, 4}

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Question 491 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set: $\{ x:x \ge 7\}$

Answer

Here $U = \{ x:x \in N\}$
Let$A = \{ x:x \geqslant 7\} = \{ 7,8,9,10,......\}$
$A' = U - A = \{ x:x \in N\} - \{ 7,8,9,10,.....\}$
= {1, 2, 3, 4, 5, 6}
= {$x:x \in N$and x < 7}

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Question 501 Mark

Taking the set of natural numbers as the universal set, write down the complement of the set:{x : x is an even natural number}

Answer

Here$U = \{ x:x \in N\}$
Let A = {x : x is an even natural number}
$A' = U - A = \{ x:x \in N\} -${x : x is an even natural number}
= {x : x is an odd natural number}

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