Sets Test

Result

Sets Test - 20

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If $n(A \cup B)=8, n(A)=6, n(B)=4$ , then $n(A\cap B)$ =

A
$2$

B
$4$

C
$6$

D
$8$

Solution

$n(A\cup B)=8\\ n(A)=6\quad ,\quad n(B)=4$

we know that
$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\$
$8=6+4-n(A\cap B)\\$
$n(A\cap B)=10-8=2$
Question 2
1 / -0

The set $\left( {A \cap B'} \right)' \cup \left( {B \cap C} \right)$ is equal to :

A
$A' \cup B \cup C$

B
$A' \cup B$

C
$A' \cup C'$

D
$A' \cap B$

Solution
Question 3
1 / -0

If A and B are any two sets, then $A \cup B$ is equal to:

A
$(A-B) \cup (B-A) \cup (A \cap B)$

B
$(A^0 \cap B^0)^0$

C
$(A-B) \cup (B-A)$

D
$A \cup (B-A)$

Solution

A & B are two sets
AᴜB = (A-B) + (A∩B) + (B-A)
Question 4
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 5
1 / -0

Let $A, B$ are two sets such that $n(A)=6, n(B)=8$ then the maximum number of elements in $n(A\cup B)$ is _________

A
$7$

B
$9$

C
$14$

D
$None$

Solution

$n(A)=6,n(B)=8$
$n(A\cup B)$ will be maximum when $A$ & $B$ are disjoint sets.
$A\cap B=\phi \\ n(A\cap B)=0\\ n(A\cup B)=n(A)+n(B)-n(A\cap B)\\ =6+8-0\\ =14\\ n(A\cup B)=14$
Question 6
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 7
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 8
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 9
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 10
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 $6)$
$B=6,12,18,24,......$
$\therefore A-B=(3,9,15,21,.....)$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Sets Test - 20

Result

Sets Test - 20

Score

-

Rank

-

SHARING IS CARING

Question 1

222

444

666

888

Solution

Question 2

A′∪B∪CA' \cup B \cup CA′∪B∪C

A′∪BA' \cup BA′∪B

A′∪C′A' \cup C'A′∪C′

A′∩BA' \cap BA′∩B

Solution

Question 3

(A−B)∪(B−A)∪(A∩B)(A-B) \cup (B-A) \cup (A \cap B)(A−B)∪(B−A)∪(A∩B)

(A0∩B0)0 (A^0 \cap B^0)^0(A0∩B0)0

(A−B)∪(B−A)(A-B) \cup (B-A)(A−B)∪(B−A)

A∪(B−A)A \cup (B-A)A∪(B−A)

Solution

Question 4

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

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

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

NoneNoneNone

Solution

Question 5

777

999

141414

NoneNoneNone

Solution

Question 6

{(1, 4)}

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

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

none of these

Solution

Question 7

1

2

3

4

Solution

Question 8

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 9

414141

434343

494949

474747

Solution

Question 10

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

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

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

none of these

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.

$2$

$4$

$6$

$8$

$A' \cup B \cup C$

$A' \cup B$

$A' \cup C'$

$A' \cap B$

$(A-B) \cup (B-A) \cup (A \cap B)$

$(A^0 \cap B^0)^0$

$(A-B) \cup (B-A)$

$A \cup (B-A)$

$\left\{\right\}$

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

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

$None$

$7$

$9$

$14$

$None$

$41$

$43$

$49$

$47$