Question 12 Marks
In the given diagram, shade the region which represents the set given underneath the diagrams$: (P ∩ Q)'$
Answer
View full question & answer→$(P ∪ Q)' =$
Questions
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35 questions · timed · auto-graded
Question 22 Marks
In the given diagram, shade the region which represents the set given underneath the diagrams $: (A ∩ B)'$
Answer
View full question & answer→$(A ∩ B)' =$
Question 32 Marks
In the given diagram, shade the region which represents the set given underneath the diagrams $: (B - A)'$
Answer
View full question & answer→$(B - A)' =$
Question 42 Marks
Two sets $A$ and $B$ are such that $A ∩ B = \Phi $. Draw a venn$-$diagram to show the relationship between $A$ and $ B$ . Shade the region representing : $B ∩ A'$
Answer
View full question & answer→$B ∩ A' =$
Question 52 Marks
Two sets $A $ and $B$ are such that $A ∩ B = \Phi $. Draw a venn$-$diagram to show the relationship between $A$ and $B$. Shade the region representing : $B - A$
Answer
View full question & answer→$B - A =$
Question 62 Marks
Two sets $A$ and $B $ are such that $A ∩ B = Φ$. Draw a venn-diagram to show the relationship between $A$ and $B$. Shade the region representing $: (A ∪ B)'$
Answer
View full question & answer→$(A ∪ B)' =$
Question 72 Marks
Two sets $A $ and $B $ are such that $A ∩ B = Φ$. Draw a venn$-$diagram to show the relationship between $A $ and $B$. Shade the region representing $: A ∪ B$
Answer
View full question & answer→$A ∪ B =$
Question 82 Marks
Draw a Venn$-$diagram to show the relationship between two sets $A$ and $B ; $ such that $A ⊆ B$, Now shade the region representing $: (A ∪ B)'$
Answer
View full question & answer→$(A ∪ B)' =$
Question 92 Marks
Draw a Venn$-$diagram to show the relationship between two sets $A$ and $B$ ; such that $A ⊆ B$, Now shade the region representing $: A ∩ B$
Answer
View full question & answer→$A ∩ B =$
Question 102 Marks
Draw a Venn$-$diagram to show the relationship between two sets $A$ and $B\ ; $ such that $A ⊆ B$, Now shade the region representing $: B' ∩ A$
Answer
View full question & answer→$B' ∩ A =$
Question 112 Marks
Draw a Venn$-$diagram to show the relationship between two sets $A$ and $B;$ such that $A ⊆ B,$ Now shade the region representing $: A ∪ B$
Answer
View full question & answer→$A ∪ B =$
Question 122 Marks
Draw a Venn$-$diagram to show the relationship between two overlapping sets $A$ and $B$. Now shade the region representing $: B - A$
Answer
View full question & answer→$B - A =$
Question 132 Marks
Draw a Venn$-$diagram to show the relationship between two overlapping sets $A$ and $B$. Now shade the region representing : $A ∪ B$
Answer
View full question & answer→$A ∪ B =$
Question 142 Marks
Draw a Venn$-$diagram to show the relationship between two overlapping sets $A$ and $B$. Now shade the region representing : $A ∩ B$
Answer
View full question & answer→$A ∩ B =$
Question 152 Marks
Using the given diagram, express the following sets in the terms of $A$ and $B. \{a, d, c, f\}$
Answer
View full question & answer→$\{a, d, c, f\} = \{A ∪ B) - \{b, e\} = \{A ∪ B) - (A ∩ B)$
Also $\{a, d, c, f\} = (A - B) ∪ (B - A)$
Also $\{a, d, c, f\} = (A - B) ∪ (B - A)$
Question 162 Marks
If $A = \{6, 7, 8, 9\}, B = \{4, 6, 8,10\}$ and $C = \{x : x ∈ N : 2 < x ≤ 7\};$ Find $ : B - B.$
Answer
View full question & answer→$A = \{6, 7, 8, 9\}$
$B = \{4, 6, 8, 10\}$
$C = \{x : x \in N : 2 < x \leq 7\}$
$= \{3, 4, 5, 6, 7\}$
$B - B = \{4, 6, 8, 10\} - \{4, 6, 8, 10\}$
$= \Phi $
$B = \{4, 6, 8, 10\}$
$C = \{x : x \in N : 2 < x \leq 7\}$
$= \{3, 4, 5, 6, 7\}$
$B - B = \{4, 6, 8, 10\} - \{4, 6, 8, 10\}$
$= \Phi $
Question 172 Marks
If $A = \{6, 7, 8, 9\}, B = \{4, 6, 8,10\}$ and $C = \{x : x \in N : 2 < x \leq 7\};$ Find $: A - (B ∪ C).$
Answer
View full question & answer→$(B ∪ C) = \{4, 6, 8, 10\} ∪ \{3, 4, 5, 6, 7\}$
$= \{3, 4, 5, 6, 7, 8,10\}$
$A - (B ∪ C) =\{6, 7, 8, 9\} - \{3, 4, 5, 6, 7, 8, 10\}$
$ = \{9\}$
$= \{3, 4, 5, 6, 7, 8,10\}$
$A - (B ∪ C) =\{6, 7, 8, 9\} - \{3, 4, 5, 6, 7, 8, 10\}$
$ = \{9\}$
Question 182 Marks
If $A = \{6, 7, 8, 9\}, B = \{4, 6, 8,10\}$ and $C = \{x : x \in N : 2 < x \leq 7\}$; Find : $B - C.$
Answer
View full question & answer→$A = \{6, 7, 8, 9\}$
$B = \{4, 6, 8, 10\}$
$C = \{x : x \in N : 2 < x \leq 7\}$
$= \{3, 4, 5, 6, 7\}$
$B - C = \{4, 6, 8, 10\} - \{3, 4, 5, 6, 7\}$
$= \{8, 10\}$
$B = \{4, 6, 8, 10\}$
$C = \{x : x \in N : 2 < x \leq 7\}$
$= \{3, 4, 5, 6, 7\}$
$B - C = \{4, 6, 8, 10\} - \{3, 4, 5, 6, 7\}$
$= \{8, 10\}$
Question 192 Marks
If $A = \{6, 7, 8, 9\}, B = \{4, 6, 8,10\}$ and $C = \{x : x \in N : 2 < x \leq 7\};$ Find $: A -B.$
Answer
View full question & answer→$A = \{6, 7, 8, 9\}$
$B = \{4, 6, 8, 10\}$
$C = \{x : x ∈ N : 2 < x ≤ 7\}$
$= \{3, 4, 5, 6, 7\}$
$A - B = \{6, 7, 8, 9\} - \{4, 6, 8, 10\}$
$= \{7, 9\}$
$B = \{4, 6, 8, 10\}$
$C = \{x : x ∈ N : 2 < x ≤ 7\}$
$= \{3, 4, 5, 6, 7\}$
$A - B = \{6, 7, 8, 9\} - \{4, 6, 8, 10\}$
$= \{7, 9\}$
Question 202 Marks
If $P = \{x : x \in W$ and $4 \leq x \leq 8\}$, and $Q = \{x : x \in N$ and $x < 6\}$. Find: $P ∪ Q$ and $P ∩ Q$.
Answer
View full question & answer→$P = (4, 5, 6, 7, 8)$
$Q = (1, 2, 3, 4, 5)$
$P ∪ Q = (1, 2, 3, 4, 5, 6, 7, 8)$
$P ∩ Q = (4, 5)$
$Q = (1, 2, 3, 4, 5)$
$P ∪ Q = (1, 2, 3, 4, 5, 6, 7, 8)$
$P ∩ Q = (4, 5)$
Question 212 Marks
Given, universal set $= \{x : \in N, 10 \leq x \leq 35\}.$
$B = \{x : x > 29\}$ Find $: B'.$
$B = \{x : x > 29\}$ Find $: B'.$
Answer
View full question & answer→Universal set $= \{x : x ∈ N, 10 ≤ x ≤ 35\}$
$= \{10, 11, 12, 13, 14, 15,....,34, 35\}$
$B = \{x : x > 29\}$
$= \{30, 31, 32, 33, 34, 35\}$
$B' = \{10, 11, 12, 13, 14, 15,.....,29\}$
$= \{x : x ≤ 29\}$
$= \{10, 11, 12, 13, 14, 15,....,34, 35\}$
$B = \{x : x > 29\}$
$= \{30, 31, 32, 33, 34, 35\}$
$B' = \{10, 11, 12, 13, 14, 15,.....,29\}$
$= \{x : x ≤ 29\}$
Question 222 Marks
Given the universal set $= \{x : x \in N$ and $x < 20\},$ find : $C = \{x : x\ $ is divisible by $4\}$
Answer
View full question & answer→$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19\}$
$∴ C = \{x : x$ is divisible by $4\}$
$C = \{4, 8, 12, 16\}$
$∴ C = \{x : x$ is divisible by $4\}$
$C = \{4, 8, 12, 16\}$
Question 232 Marks
Write two sets$ A$ and $B $ such that $A ⊆ B$ and $B ⊆ A$. State the relationship between sets $A$ and $B$.
Answer
View full question & answer→Let $A = \{$Letters of $\text{TALE\}}$
$B = \{$Letters of $\text{LATE\}}$
Here $A ⊆ B,$ and $B ⊆ A$
$∴ A = B$
$B = \{$Letters of $\text{LATE\}}$
Here $A ⊆ B,$ and $B ⊆ A$
$∴ A = B$
Question 242 Marks
Let $M = \{$letters of the word $\text{REAL\}}$ and $N = \{$letters of the word $\text{LARE\}}$. Write sets $M $ and $N$ in roster form and then state whether $M = N$ is true.
Answer
View full question & answer→$M = \{$letters of theword $\text{REAL\}}$
$= \text\{{R, E, A, L\}}$
and $N = \{$letters of the word $\text{LARE\}}$
$= \text\{{L, A, R, E\}}$
$M = N$ is true : Yes
$= \text\{{R, E, A, L\}}$
and $N = \{$letters of the word $\text{LARE\}}$
$= \text\{{L, A, R, E\}}$
$M = N$ is true : Yes
Question 252 Marks
Let $M = \{$letters of the word $\text{REAL\}}$ and $N = \{$letters of the word $\text{LARE\}}$. Write sets $M$ and $N $ in roster form and then state whether $N ⊆ M$ is true.
Answer
View full question & answer→$M = \{$letters of theword $\text{REAL\}}$
$= \text\{{R, E, A, L\}}$
and $N = \{$letters of the word $\text{LARE\}}$
$= \text\{{L, A, R, E\}}$
$N ⊆ M$ is true : Yes
$= \text\{{R, E, A, L\}}$
and $N = \{$letters of the word $\text{LARE\}}$
$= \text\{{L, A, R, E\}}$
$N ⊆ M$ is true : Yes
Question 262 Marks
Let$ M = \{$letters of the word $\text{REAL\}}$ and $N = \{$letters of the word $\text{LARE\}}$. Write sets $M$ and $N$ in roster form and then state whether$; M ⊆ N$ is true.
Answer
View full question & answer→$M = \{$letters of theword $\text{REAL\}}$
$= \text\{{R, E, A, L\}}$
and $N =\ \{$letters of the word $\text{LARE\}}$
$=\text\{{L, A, R, E\}}$
$M ⊆ N$ is true : Yes
$= \text\{{R, E, A, L\}}$
and $N =\ \{$letters of the word $\text{LARE\}}$
$=\text\{{L, A, R, E\}}$
$M ⊆ N$ is true : Yes
Question 272 Marks
Given universal set $= \{x ∈ Z : -6 < x ≤ 6\}. P =\{x : x$ is a non$-$positive number$\}$. Find $: P'$
Answer
View full question & answer→Universal set $= \{x ∈ Z : -6 < x ≤ 6\}$
$= \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$
$P = \{x : x$ is a non-positive number$\}$
$= \{-5, -4, -3, -2, -1\}$
$P' = \{1, 2, 3, 4, 5, 6\}$
$= \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$
$P = \{x : x$ is a non-positive number$\}$
$= \{-5, -4, -3, -2, -1\}$
$P' = \{1, 2, 3, 4, 5, 6\}$
Question 282 Marks
Given universal set $= \{x ∈ Z : -6 < x ≤6\}$.
$N = \{n : n$ is non-negative number$\}$ Find $: N'$
$N = \{n : n$ is non-negative number$\}$ Find $: N'$
Answer
View full question & answer→Universal set $= \{x ∈ Z ; -6 < x ≤ 6\}$
$= \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$
$N = \{n : n$ is a non-negative number$\}$
$= \{0, 1, 2, 3, 4, 5, 6\}$
$N' = \{-5, -4, -3, -2, -1\}$
$= \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}$
$N = \{n : n$ is a non-negative number$\}$
$= \{0, 1, 2, 3, 4, 5, 6\}$
$N' = \{-5, -4, -3, -2, -1\}$
Question 292 Marks
State if the following set is a finite set or an infinite set$:\{x : x = 3n – 2, n \in W, n \leq 8\}$
Answer
View full question & answer→$\{x : x = 3n – 2, n ∈ W, n ≤ 8\}$
Substituting the value of $n = (0, 1, 2, 3, 4, 5, 6, 7$ and $8)$ we get
$= \{-2, 1, 4, 7, 10, 13, 16, 19, 22\}$
It is finite set.
Substituting the value of $n = (0, 1, 2, 3, 4, 5, 6, 7$ and $8)$ we get
$= \{-2, 1, 4, 7, 10, 13, 16, 19, 22\}$
It is finite set.
Question 302 Marks
State, if the following pair of a set is equivalent or not: Set of whole numbers and set of multiples of $3$.
Answer
View full question & answer→Set of whole numbers, has infinite number of elements. Set of multiples of $3$, has infinite number of element.
Set of whole numbers and set of multiples of $3 $ are equivalent because both these sets have infinite number of elements.
Set of whole numbers and set of multiples of $3 $ are equivalent because both these sets have infinite number of elements.
Question 312 Marks
State, if the following pair of a set is equivalent or not : Set of integers and set of natural numbers.
Answer
View full question & answer→Check whether the given pair of sets are equivalent
Given: Set of integers and set of natural numbers.
A set of integers is $\{...−1,0,1,2,3,....\},$
which is clearly an infinite set as it has uncountable number of elements.
A set of natural numbers is $\{0, 1, 2, 3,......\}$
which is also an infinite set as it has an uncountable number of elements.
As both the sets have the same number of elements, the two sets are equivalent sets.
Hence, given sets are equivalent.
Given: Set of integers and set of natural numbers.
A set of integers is $\{...−1,0,1,2,3,....\},$
which is clearly an infinite set as it has uncountable number of elements.
A set of natural numbers is $\{0, 1, 2, 3,......\}$
which is also an infinite set as it has an uncountable number of elements.
As both the sets have the same number of elements, the two sets are equivalent sets.
Hence, given sets are equivalent.
Question 322 Marks
Are the sets $A = \{b, c, d, e\}$ and $B = \{x : x$ is a letter in the word $\text{‘MASTER’\}}$ joint?
Answer
View full question & answer→$A = \{b,c,d,e\}$
$B = \{x : x$ is a letter in the word $\text{"MASTER"\}}$
$∴ B = \{m, a ,s, t, e, r\}$
Hence set $A $ and set $B $ are joint because these sets have element e in common.
$B = \{x : x$ is a letter in the word $\text{"MASTER"\}}$
$∴ B = \{m, a ,s, t, e, r\}$
Hence set $A $ and set $B $ are joint because these sets have element e in common.
Question 332 Marks
State the following sets are finite or infinite:$A = \{x : x \in Z$ and $x < 10\}$
Answer
View full question & answer→$A = \{x : x \in Z$ and $x < 10\}$
$= \{....., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$
$= \{9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, .....\}$
$\therefore $ It is an infinite set.
$= \{....., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$
$= \{9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, .....\}$
$\therefore $ It is an infinite set.
Question 342 Marks
Find the cardinal number of the following sets : $A_2= \{x : x \in N$ and $3 ≤ x <7\}$
Answer
View full question & answer→$A_2= \{x : x \in N$ and $3 ≤ x <7\}$
$= {3, 4, 5, 6}$
$∴$ Cardinal number of set $A_2 = 4$
$= {3, 4, 5, 6}$
$∴$ Cardinal number of set $A_2 = 4$
Question 352 Marks
Write the set of prime factors of $3234.$
Answer
$3234 = 2 x\times 3 x\times 7 x\times 7 x\times 11$
$\therefore $Set of prime factors of $3234 = \{2, 3, 7, 11\}$
View full question & answer→| $2$ | $3234$ |
| $3$ | $1617$ |
| $7$ | $539$ |
| $7$ | $77$ |
| $11$ |
$\therefore $Set of prime factors of $3234 = \{2, 3, 7, 11\}$