Let A = θ ∈ R : 1 3 sin θ + 2 3 cos θ 2 = 1 3 sin 2 θ + 2 3 cos 2 θ . Then

A ∩ 0 , π has exactly one point

A ∩ 0 , π has exactly two points

A ∩ 0 , π has more than two points

EASY

Earn 100

If $A$ and $B$ are two sets such that $A \subset B$ , then what is $A \cup B ?$

33.33% studentsanswered this correctly

Important Questions on Theory of Sets

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

A

and

B

be two sets such that

A \cap X = B \cap X = ϕ

and

A \cup X = B \cup X

for same set

X

. Then,

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

A survey shows that

73 %

of the persons working in an office like coffee, whereas

65 %

like tea. If

x

denotes the percentage of them, who like both coffee and tea, then

x

cannot be:

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

n (A) = 3, n (B) = 6

and

A \subseteq B,

then the number of elements in

(A \cup B)

is equal to

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

In a class of

175

students the following data shows the number of students opting one or more subjects. Mathematics

100

, Physics

70

, Chemistry

40

, Mathematics and Physics

30,

Mathematics and Chemistry

28

, Physics and Chemistry

23

, Mathematics, physics and Chemistry

18

. The number of students who have opted Mathematics alone is

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

A = {x | x \in N, x

is a prime number less than

12}

and

B = {x |

x \in N

x

is factor of

10}

, then

A \cap B

=

…

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

HARD

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's then $n$ is equal to :

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

In an examination,

53 %

of the candidates failed in science and

48 %

failed in mathematics. If

40 %

failed in both subjects, what percentage passed in both subjects ?

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

U

is the universal set with

100

elements;

A

and

B

are two sets such that

n (A) = 50, n (B) = 60

n (A \cap B) = 20

then

n (A^{'} \cap B^{'}) =

HARD

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

A

and

B

be finite sets such that

n (A - B) = 18, n (A \cap B) = 25

and

n (A \cup B) = 70

. Then

n (B)

is equal to

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

A = {n \in N : n

is a

3 -

digit number

}

B = \{9 k + 2 : k \in N\}

and

C = \{9 k + l : k \in N\}

for some

l (0 < l < 9)

. If the sum of all the elements of the set

A \cap (B \cup C)

274 \times 400,

then

l

is equal to

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

Two newspapers

A

and

B

are published in a city. It is known that

25 %

of the city population reads

A

and

20 %

reads

B

while

8 %

reads both

A

and

B .

Further,

30 %

of those who read

A

but not

B

look into advertisements and

40 %

of those who read

B

but not

A

also look into advertisements, while

50 %

of those who read both

A

and

B

look into advertisements. Then the percentage of the population who look into advertisements is:

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Question Image

HARD

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

A = \{θ \in R : {(\frac{1}{3} \sin θ + \frac{2}{3} \cos θ)}^{2} = \frac{1}{3} \sin^{2} θ + \frac{2}{3} \cos^{2} θ\}

. Then

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as

$S_{1} = {z \in ℂ : | z - 1 | \leq \sqrt{2}},$

$S_{2} = {z \in ℂ : R e ((1 - i) z) \geq 1}$ and

$S_{3} = {z \in ℂ : I m (z) \leq 1} .$

Then, the set $S_{1} \cap S_{2} \cap S_{3}$

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

A = \{n \in N ∣ n^{2} \leq n + 10, 000\}, B = \{3 k + 1 ∣ k \in N\}

and

C = \{2 k ∣ k \in N\},

then the sum of all the elements of the set

A \cap (B - C)

is equal to ________.

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

n (A) = 61, n (B) = 95, n (A - B) = 25,

then

n (A \cup B)

is equal to

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

A survey shows that

63 %

of the people in a city read newspaper

A

whereas

76 %

read news paper

B

. If

x %

of the people read both the newspapers, then a possible value of

x

can be:

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

Let

X = \{n \in N : 1 \leq n \leq 50\}

. If

A = \{n \in X : n is a multiple of 2\}

and

B = \{n \in X : n is a multiple of 7\}

, then the number of elements in the smallest subset of

X

, containing both

A

and

B

, is.

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

In a class of

140

students numbered

1

140

, all even numbered students opted Mathematics course, those whose number is divisible by

3

opted Physics course and those whose number is divisible by

5

opted Chemistry course. Then the number of students who did not opt for any of the three courses is:

If A and B are two sets such that A⊂B, then what is A∪B?

Important Questions on Theory of Sets

Learn and Prepare for any exam you want !

If $A$ and $B$ are two sets such that $A \subset B$ , then what is $A \cup B ?$