Sets Test

Result

Sets Test - 1

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

In a society of 1250 families, 500 read news paper X, 300 read newspaper Y and 150 read both the newspapers. What is the number of families that read neither of the newspapers?

A
600

B
550

C
500

D
450

Solution

Let A and B denote the set of families who reads newspaper X and Y respectively.

Given, n (A) = 500, n (B) = 300 and n (A ∩ B) = 150

Now, n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

⇒ n (A ∪ B) = 500 + 300 – 150 = 650

∴ Number of families who read none of the newspapers

= 1250 – 650

= 600
Question 2
1 / -0

Two finite sets A and B have x and y elements respectively. The number of elements in the power set of A is 120 more than the number of elements in the power set of B. What are the values of x and y respectively?

A
3 and 7

B
7 and 3

C
4 and 6

D
6 and 4

Solution

Number of elements in the power set of A = 2^x

Number of elements in the power set of B = 2^y

Given: 2^x = 2^y + 120

⇒ 2^x − 2^y= 120

⇒ 2^y (2^x−y − 1) = 2 × 2 × 2 × 3 × 5

⇒ 2^y (2^x−y − 1) = 2³ (2⁴ −1)

⇒ y = 3 and x − y = 4

∴ x = y + 4 = 3 + 4 = 7
Question 3
1 / -0

Use the following information to answer the next question.

Three sets, A, B, and C, are defined as

A = {x: x = 5n, n ∈ N and n < 6}

B = {y: y = 3n + 1, n ∈ N, and n ≤ 8}

C = (z: z = 6n − 2, n ∈ N, and n ≤ 4}

Which set is equal to the set A − (B ∩ C)?

A
{5, 15, 20}

B
{5, 15, 20, 25}

C
{4, 5, 15, 16, 22, 25}

D
{4, 5, 10, 15, 16, 20, 22, 25}

Solution

A = {x: x = 5n, n ∈ N and n < 6} = {5, 10, 15, 20, 25}

B = {y: y = 3n + 1, n ∈ N, and n ≤ 8} = {4, 7, 10, 13, 16, 19, 22, 25}

C = (z: z = 6n − 2, n ∈ N, and n ≤ 4} = {4, 10, 16, 22}

∴B ∩ C = {4, 7, 10, 16, 19, 22, 25}∩ {4, 10, 16, 22} = {4, 10, 16, 22}

Thus, A − (B ∩ C) = {5, 10, 15, 20, 25} − {4, 10, 16, 22} = {5, 15, 20, 25}
Question 4
1 / -0

Which of the following is not a set?

A
The collection of all universities in India

B
The collection of all hard working students of a particular school

C
Thecollection of all members of the Lower house of the Parliament of India

D
The collection of all girls of a particular co-educational school

Solution

The collection of all hard working students of a particular school is not well

defined because the criterion for determining a student as hard working may

vary from person to person.

Therefore, this collection is not a set.
Question 5
1 / -0

Use the following information to answer the next question.

In a survey of 500 students in a school, 260 students preferred to watch comedy movie, 280 students preferred to watch action movie, and 20 students preferred to watch neither comedy nor action movie.

How many students preferred to watch both the types of movies?

A
30

B
40

C
60

D
70

Solution

Let U be the set of all surveyed students in the School, C be the set of students preferring to watch comedy movie, and A be the set of students preferring to watch action movie.

Then, according to the given information,

n (U) = 500, n (C) = 260, n (A) = 280, n (C′ ∩ A′) = 20

n (C ∪ A)′ = 20

⇒ n (U) − n (C ∪ A) = 20

⇒ 500 − n (C ∪ A) = 20

⇒ n (C ∪ A) = 500 − 20 = 480

It is known that, n (C ∪ A) = n (C) + n (A) − n (C ∩ A)

∴480 = 260 + 280 − n (C ∩ A)

⇒ n (C ∩ A) = 260 + 280 − 480 = 60

Thus, 60 students prefer to watch both types of movies.
Question 6
1 / -0

If A ∪ B = C, A ∩ B = Φ and B ⊂ A then which of the following is true?

A
C − B = B

B
(C − B) = (A − B) ∪ B

C
B = C

D
None of these

Solution

Given, A ∪ B = C
⇒ C − B = (A ∪ B) − B
We can write (A ∪ B) − B = (A ∪ B) ∩ B′

= (A ∪ B) ∩ B′

= (A ∩ B′) ∪ (B ∩ B′)

= (A ∩ B′) ∪ Φ

= A ∩ B′

= A − B

= A ...(1) [ ∵A ∩ B = Φ]

Also, B ⊂ A

Now, (A − B) ∪ B = (A ∩ B′) ∪ B

= (A ∪ B) ∩ (B′ ∪ B)

= (A ∪ B) ∩ U

= A ∪ B

= A ...(2) [∵B ⊂ A ⇒ A ∪ B = A]

From (1) and (2), we have

C − B = (A − B) ∪ B

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Sets Test - 1

Result

Sets Test - 1

Score

-

Rank

-

SHARING IS CARING

Question 1

600

550

500

450

Solution

Question 2

3 and 7

7 and 3

4 and 6

6 and 4

Solution

Question 3

{5, 15, 20}

{5, 15, 20, 25}

{4, 5, 15, 16, 22, 25}

{4, 5, 10, 15, 16, 20, 22, 25}

Solution

Question 4

The collection of all universities in India

The collection of all hard working students of a particular school

Thecollection of all members of the Lower house of the Parliament of India

The collection of all girls of a particular co-educational school

Solution

Question 5

30

40

60

70

Solution

Question 6

C − B = B

(C − B) = (A − B) ∪ B

B = C

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.