Set Theory Test 2

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Set Theory Test 2

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Weekly Quiz Competition

Question 1
1 / -0

If $$\displaystyle Q=\left\{ x:x=\frac { 1 }{ y } ,where\ \ y\ \in \ N \right\} $$, then find the correct one.

A
$$\displaystyle 0\quad \in \quad Q$$

B
$$\displaystyle 1\quad \in \quad Q$$

C
$$\displaystyle 2\quad \in \quad Q$$

D
$$\displaystyle \frac { 2 }{ 3 } \quad \in \quad Q$$

Solution

(A) Since $$\displaystyle y\neq\frac{1}{0}$$ then $$0\notin Q$$

(B) Since $$\displaystyle y=\frac{1}{2}$$ as $$1\in N$$ then $$1\in Q$$

(C) Since $$\displaystyle y\neq\frac{1}{2}$$ as $$\displaystyle\frac{1}{2}\notin N$$ then $$2\notin Q$$

(D) Since $$\displaystyle y\neq\frac{3}{2}$$ as $$\displaystyle\frac{3}{2}\notin N$$ then $$\displaystyle\frac{2}{3}\notin Q$$
Question 2
1 / -0

Which set is the subset of the set containing all the whole numbers?

A
$$\{1,2,3,4,.......\}$$

B
$$\{1\}$$

C
$$\{0\}$$

D
All of the above

Solution

Null set is the subset of all given sets as it can lie in all sets.
Question 3
1 / -0

In an examination $$70\%$$ students passed both in Mathematics and Physics $$85\%$$ passed in Mathematics and $$80\%$$ passed in Physics If $$30$$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to :

A
$$900$$

B
$$600$$

C
$$150$$

D
$$100$$

Solution

Student passed in atleast one subject
$$= n$$ $$\displaystyle \left ( P\cup M \right )= n\left ( P \right )+n\left ( M \right )-n\left ( P\cup M \right )$$
$$= 80 + 85 - 70 = 95$$
$$\displaystyle \therefore $$ $$5\%$$ student failed in both the subjects
$$\displaystyle \Rightarrow $$$$5\%$$ of total students $$= 30$$
$$\displaystyle \Rightarrow $$Total students = $$\displaystyle \frac{30\times 100}{5}= 600$$
Question 4
1 / -0

If $$n(A) = 65, n(B) = 32$$ and $$\displaystyle n\left ( A\cap B \right )=14 $$, then $$\displaystyle n\left ( A\Delta B \right ) $$ equals

A
$$65$$

B
$$47$$

C
$$97$$

D
$$69$$

Solution

$$\displaystyle n(A\Delta B)=n (A-B)+n(B-A)$$
$$\displaystyle \therefore A\Delta B=(A-B)\cup (B-A)$$
$$\Rightarrow A\Delta B=\displaystyle n(A)-n(A\cap B)+n(B)-n(A\cap B)$$
$$\Rightarrow A\Delta B =n(A)+n(B)-2n(A\cap B)=65+32-2\times 14=69$$
Hence, $$A\Delta B=69$$
Question 5
1 / -0

If $$X$$ and $$Y$$ are any two non empty sets then what is $$\displaystyle \left ( X-Y \right )'$$ equal to?

A
$$X' - Y'$$

B
$$\displaystyle {X}'\cap Y $$

C
$$\displaystyle {X}'\cup Y $$

D
$$X - Y'$$

Solution

$$X - Y$$ $$\displaystyle =\left \{ x :x \in X,x\notin Y \right \}$$
$$\displaystyle =\left \{ x :x \in X,x\in Y'\right \}$$
$$\displaystyle \Rightarrow \left \{ x : x\in X\cap Y' \right \}$$
$$\displaystyle \Rightarrow \left ( X-Y \right )'=(X\cap Y)'$$
= $$\displaystyle X'\cup (Y')=X'\cup Y$$
Question 6
1 / -0

If $$n(A) = 115$$, $$n(B) = 326$$, $$n(A - B) = 47$$ then $$\displaystyle n\left ( A\cup B \right )$$ is equal to

A
$$373$$

B
$$165$$

C
$$370$$

D
None

Solution

$$n(A)=115,n(B)=326$$
$$n(A-B)=47$$
$$n(A)=n(A-B)+n(A\cap B)$$
$$n(A\cap B)=n(A)-n(A-B)$$
$$\therefore n(A\cap B)=115-47=68$$
$$\therefore n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$\Rightarrow n(A\cup B)=115+326-68$$
$$\Rightarrow n(A\cup B)=373$$
Question 7
1 / -0

If $$A$$ and $$B$$ are non empty sets and A' and B' represents their compliments respectively then

A
$$A - B = A' - B'$$

B
$$A - A' = B - B'$$

C
$$A - B = B' - A'$$

D
$$A - B' = A' - B$$

Solution

Let $$ U \to$$ Universal set
$$X\to U - (A+B) $$
$$B'=X+A$$
$$A'=X+B$$
$$B'-A'= X+A-(X+B)$$
$$=X+A-X-B$$
$$B'-A'=A-B$$
Question 8
1 / -0

If $$\displaystyle \xi =\left \{ 2,3,4,5,6,7,8,9,10,11 \right \}$$
$$\displaystyle A =\left \{ 3,5,7,9,11 \right \}$$
$$\displaystyle B =\left \{ 7,8,9,10,11 \right \}$$, then find $$(A - B)'$$

A
$$(A - B)' = \{2,4,6,7,8,9,10,11\}$$

B
$$(A - B)' = \{2,4,6,7,8,9,11\}$$

C
$$(A - B)' = \{2,4,6,7,9,10,11\}$$

D
$$(A - B)' = \{2,4,6,8,9,10,11\}$$

Solution

$$A - B = \{3, 5\}$$
$$(A - B)' = \{2,4,6,7,8,9,10,11\}$$
Question 9
1 / -0

The set of all those elements of A and B which are common to both is called

A
union of two sets

B
intersection of two sets

C
disjoint sets

D
none of these

Solution

The set of all those elements of A and B which are common to both is called A intersection B=$$A\cap B$$
Question 10
1 / -0

Given $$K=\left \{B, A, N, T, I\right \}$$. Then the number of subsets of K, that contain both A, N is

A
8

B
16

C
24

D
32

Solution

$$K=\left\{B,A,N,T,I\right\}$$
The number of subset of K that contain both A ,N=$$2^2=8$$

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Re-Attempt Weekly Quiz Competition

Set Theory Test 2

Result

Set Theory Test 2

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SHARING IS CARING

Question 1

$$\displaystyle 0\quad \in \quad Q$$

$$\displaystyle 1\quad \in \quad Q$$

$$\displaystyle 2\quad \in \quad Q$$

$$\displaystyle \frac { 2 }{ 3 } \quad \in \quad Q$$

Solution

Question 2

$$\{1,2,3,4,.......\}$$

$$\{1\}$$

$$\{0\}$$

All of the above

Solution

Question 3

$$900$$

$$600$$

$$150$$

$$100$$

Solution

Question 4

$$65$$

$$47$$

$$97$$

$$69$$

Solution

Question 5

$$X' - Y'$$

$$\displaystyle {X}'\cap Y $$

$$\displaystyle {X}'\cup Y $$

$$X - Y'$$

Solution

Question 6

$$373$$

$$165$$

$$370$$

None

Solution

Question 7

$$A - B = A' - B'$$

$$A - A' = B - B'$$

$$A - B = B' - A'$$

$$A - B' = A' - B$$

Solution

Question 8

$$(A - B)' = \{2,4,6,7,8,9,10,11\}$$

$$(A - B)' = \{2,4,6,7,8,9,11\}$$

$$(A - B)' = \{2,4,6,7,9,10,11\}$$

$$(A - B)' = \{2,4,6,8,9,10,11\}$$

Solution

Question 9

union of two sets

intersection of two sets

disjoint sets

none of these

Solution

Question 10

8

16

24

32

Solution

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