Sets Test

Result

Sets Test - 21

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Weekly Quiz Competition

Question 1
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 2
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 3
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 4
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 , $$ B \subset C $$
Question 5
1 / -0

If $$ A = \left \{ 2 , 4, 6, 8 \right \} $$ and $$ B = \left \{ 1, 4, 7, 8 \right \}$$ then A - B and B - A will be respectively:

A
$$\left \{ 2 ,6 \right \} ; \left \{ 1, 7 \right \}$$

B
$$\left \{ 1, 7 \right \} ; \left \{ 4 , 8 \right \}$$

C
$$\left \{ 1, 7 \right \} ; \left \{ 2, 6 \right \}$$

D
$$\left \{ 4, 8 \right \} ; \left \{ 1, 7 \right \}$$

Solution

$$ A = \left \{ 2 , 4, 6, 8 \right \}$$ and $$ B = \left \{ 1, 4, 7, 8 \right \}$$
$$ A - B = \left \{ 2, 6 \right \} $$ and $$ B - A = \left \{ 1 , 7 \right \}$$
Hence , option (A) is correct
Question 6
1 / -0

If $$ A = \left \{ 1, 2, 3, 4, 5, 6 \right \} , B = \left \{ 2, 4, 6, 8 \right \}$$, then A - B will be :

A
$$\left \{1, 3, 5, 8 \right \}$$

B
$$\left \{ 1, 3, 5 \right \}$$

C
$$\left \{1, 2, 3, 4, 5, 6, 8 \right \}$$

D
= { }

Solution

Given , $$ A = \left \{ 1, 2, 3, 4, 5, 6 \right \}$$ and $$ B = \left \{2, 4, 6, 8 \right \}$$
A - B means A contains the element which is not present in B.
Thus, $$A - B = \left \{ 1, 3, 5 \right \}$$
Hence , option (B) is correct.
Question 7
1 / -0

If $$A= $${1,2,3};$$ B=$${4,5}. then $$A-B=$${1,2,3} number cancellation of numbers in A and B

A
{4,5}

B
{1,2,3,4,5}

C
$$\phi $$

D
{1,2,3}

Solution
Question 8
1 / -0

In an examination, $$34\%$$ of the candidates fail in Arithmetic and $$42\%$$ in English. If $$20\%$$ fail in Arithmetic and English, the percentage of those passing in both subjects is :

A
$$44$$

B
$$45$$

C
$$46$$

D
$$47$$

Solution

Let $$A$$ denote students fail in Arithmetic, $$B$$ denote students fail in English
$$n(A)=34$$
$$n(B)=42$$
$$n(A \cap B)=20$$
$$n(A \cup B) = n(A) + n(B) - n(A \cap B) = 34+42-20=56$$
$$n(A \cup B)' = 100 - n(A \cup B) = 100-56=44$$
Question 9
1 / -0

The smallest set $$A$$ such that $$A\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $$ is

A
$$\left\{ 2,3,5 \right\} $$

B
$$\left\{ 3,5,9 \right\} $$

C
$$\left\{ 1,2,5,9 \right\} $$

D
$$\left\{ 1,2 \right\} $$

Solution

$$A\cup \{1,2\}=\{1,2,3,5,9\}$$
Thus
$$A=\{1,2,3,5,9\}-\{1,2\}$$

Hence
$$A=\{3,5,9\}$$
Question 10
1 / -0

If A = {1, 2, 3} B = {4, 5}, then find A - B.

A
{1, 4, 5}

B
{1, 4, 3}

C
{1, 2, 3}

D
{4, 5}

Solution

Given, $$A=\{1,2,3\}$$ and $$B=\{4,5\}$$.
Since $$A$$ and $$B$$ are two disjoint sets i.e. $$A\cap B=\phi$$ then we've,
$$A-B$$
$$=\{1,2,3\}$$.

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Re-Attempt Weekly Quiz Competition

Sets Test - 21

Result

Sets Test - 21

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SHARING IS CARING

Question 1

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

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

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

$${ 2 }^{ n }$$

Solution

Question 2

$$10$$

$$20$$

$$512$$

$$1024$$

Solution

Question 3

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 4

$$ A \subset B $$

$$ B \subset C $$

$$ C \subset B $$

$$ A \subset C $$

Solution

Question 5

$$\left \{ 2 ,6 \right \} ; \left \{ 1, 7 \right \}$$

$$\left \{ 1, 7 \right \} ; \left \{ 4 , 8 \right \}$$

$$\left \{ 1, 7 \right \} ; \left \{ 2, 6 \right \}$$

$$\left \{ 4, 8 \right \} ; \left \{ 1, 7 \right \}$$

Solution

Question 6

$$\left \{1, 3, 5, 8 \right \}$$

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

$$\left \{1, 2, 3, 4, 5, 6, 8 \right \}$$

= { }

Solution

Question 7

{4,5}

{1,2,3,4,5}

$$\phi $$

{1,2,3}

Solution

Question 8

$$44$$

$$45$$

$$46$$

$$47$$

Solution

Question 9

$$\left\{ 2,3,5 \right\} $$

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

$$\left\{ 1,2,5,9 \right\} $$

$$\left\{ 1,2 \right\} $$

Solution

Question 10

{1, 4, 5}

{1, 4, 3}

{1, 2, 3}

{4, 5}

Solution

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