Set Theory Test 8

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Set Theory Test 8

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Weekly Quiz Competition

Question 1
1 / -0

If $$A=\left\{2, 4, 6, 8, 10\right\}, B=\left\{1, 3, 5, 7, 9\right\}$$, then $$A-B$$ =____________

A
$$\left\{\right\}$$

B
$$\left\{2, 4, 6, 8, 10\right\}$$

C
$$\left\{1, 3, 5, 7, 9\right\}$$

D
$$None$$

Solution

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

If A={1, 2, 4}, B={2, 4, 5}, C={2, 5}, then (A-C)$$\times$$(B-C) is equal to

A
{(1, 4)}

B
{(1, 4), (4, 4)}

C
{(4, 1), (4, 4)}

D
none of these

Solution

$$A=\{1, 2, 4\}$$, $$B=\{2, 4, 5\}$$, $$C=\{2, 5\}$$
$$A-C=\{1, 4\}$$
$$B-C=\{4\}$$
$$(A-C)\times (B-C)=\{1, 4\}\times \{4\}$$
$$=\{1, 4\}, \{4, 4\}$$.
Question 3
1 / -0

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

A
1

B
2

C
3

D
4

Solution

We know,
$$n(A \cap B)=n(A)+n(B)-n(A \cup B)$$
$$n(A \cap B)=17+23-38=2$$
Question 4
1 / -0

Which of the following is set ?

A
The collection of months having names starting with J.

B
The collection of smart boys in your class.

C
The collection of most talented persons.

D
The collection of sand grains in a Earth.

Solution

As the collection of months having names starting with J is well defined. So, it's a set. Rest are not well defined , hence are not set.
Question 5
1 / -0

If X and Y are two sets such that $$n(X)=45, n(X \cup Y)=76, n(X \cap Y)=12,$$ find $$n(Y)$$.

A
$$41$$

B
$$43$$

C
$$49$$

D
$$47$$

Solution

$$n(X \cup Y)=n(X) +n(Y)-n(X \cap Y)$$
$$76=45+n(Y)-12$$
$$n(Y)=43$$
Question 6
1 / -0

If A={$$x\in N$$ : xis a multiple of 3} and
B={$$x\in N$$ : is a multiple of 6}, then A-B is equal to

A
{6, 12, 18,.......}

B
{3, 6, 9, 12,.........}

C
{3, 9, 15, 21,.........}

D
none of these

Solution

$$A=x\epsilon \quad N:x$$ is a multiple of $$3$$.
$$A=3,6,9,12,15,18,......$$
$$B=(x\quad \epsilon N:x$$ is a multiple of $$6)$$
$$B=6,12,18,24,......$$
$$\therefore A-B=(3,9,15,21,.....)$$
Question 7
1 / -0

The number of subsets of the set $$A=\{ { a }_{ 1 },{ a }_{ 2 },.........{ a }_{ n }\} $$ which contain even number of elements is

A
$${ 2 }^{ n-1 }$$

B
$${ 2 }^{ n }-1$$

C
$${ 2 }^{ n }-2$$

D
$${ 2 }^{ n }$$

Solution

The total no of subsets of $$A$$ is the cardinality of the power set of $$A$$.

So, if $$|A|=n$$ then $$|P(A)|=2^n$$.

Therefore total no of subsets of $$A$$ is $$2^n$$.

Similarly,

The even number of events is given by, $$2^{n-1}$$
Question 8
1 / -0

Let $$S=\{2,4,6,8,......20\}$$. What is the maximum number of subsets does $$S$$ have ?

A
$$10$$

B
$$20$$

C
$$512$$

D
$$1024$$

Solution

Given,

$$S={2,4,6,8........,20}$$

There are a total of $$10$$ elements.

Therefore we have $$2^{10}=1024$$ subsets.
Question 9
1 / -0

Which of the following collections is a set?

A
Collection of all tasty fruits

B
Collection of all good football players of your school

C
Collection of all months of a year

D
Collection of $$5$$ most intelligent students of your class.

Solution

Collection of all months of a year is a set If we denote the given set, then
$$A =\{\text{January, February, March, April, ........December}\}$$
Question 10
1 / -0

For sets $$\phi , A = \left \{ 1,3 \right \} = B = \left \{ 1, 5, 9 \right \} , C = \left \{ 1, 5, 7, 9 \right \}$$ True option is

A
$$ A \subset B $$

B
$$ B \subset C $$

C
$$ C \subset B $$

D
$$ A \subset C $$

Solution

Option (B) is correct , because all the elements of set $$B = \left \{ 1, 5, 9 \right \}$$ is present in set $$ C = (1, 5, 7, 9) $$ Hence , $$ B \subset C $$

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Set Theory Test 8

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Set Theory Test 8

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Question 1

$$\left\{\right\}$$

$$\left\{2, 4, 6, 8, 10\right\}$$

$$\left\{1, 3, 5, 7, 9\right\}$$

$$None$$

Solution

Question 2

{(1, 4)}

{(1, 4), (4, 4)}

{(4, 1), (4, 4)}

none of these

Solution

Question 3

1

2

3

4

Solution

Question 4

The collection of months having names starting with J.

The collection of smart boys in your class.

The collection of most talented persons.

The collection of sand grains in a Earth.

Solution

Question 5

$$41$$

$$43$$

$$49$$

$$47$$

Solution

Question 6

{6, 12, 18,.......}

{3, 6, 9, 12,.........}

{3, 9, 15, 21,.........}

none of these

Solution

Question 7

$${ 2 }^{ n-1 }$$

$${ 2 }^{ n }-1$$

$${ 2 }^{ n }-2$$

$${ 2 }^{ n }$$

Solution

Question 8

$$10$$

$$20$$

$$512$$

$$1024$$

Solution

Question 9

Collection of all tasty fruits

Collection of all good football players of your school

Collection of all months of a year

Collection of $$5$$ most intelligent students of your class.

Solution

Question 10

$$ A \subset B $$

$$ B \subset C $$

$$ C \subset B $$

$$ A \subset C $$

Solution

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