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

HARD

Earn 100

A class has $175$ students. The following table shows the number of students studying one or more of the following subjects in this case :

Subject No. of students

Mathematics $100$

Physics $70$

Chemistry $46$

Mathematics and Physics $30$

Mathematics and Chemistry $28$

Physics and Chemistry $23$

Mathematics, Physics and Chemistry $18$

How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone? What is the number of students who have not offered any of these three subjects?

Important Questions on Set Theory and Relations

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

If $A = {1, 2, 3, 4, 5}$ and $B = {2, 4, 6}$ , then $A - B =$

EASY

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

A \subset B,

then

A Δ B

is equal to

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of 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

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of 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>Set Theory and Relations>Algebra of 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.

EASY

Mathematics>Algebra>Set Theory and Relations>Algebra of 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:

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

In a group of

100

persons,

80

people can speak Malayalam and

60

can speak English. Then the number of people who speak English only is

EASY

Mathematics>Algebra>Set Theory and Relations>Algebra of 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>Set Theory and Relations>Algebra of 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

=

…

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

A = \{x \in R : |x| < 2\}

and

B = \{x \in R : |x - 2| \geq 3\};

then

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

Consider the two sets:

A = {m \in R :

both the roots of

x^{2} - (m + 1) x + m + 4 = 0

are real

}

and

B = [- 3, 5)

Which of the following is not true?

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

In a certain town,

25 %

of the families own a phone and

15 %

own a car;

65 %

families own neither a phone nor a car and

2000

families own both a car and a phone. Consider the following three statements:

(i)

5 %

families own both a car and a phone.

(i i)

35 %

families own either a car or a phone.

(i i i)

40000

families live in the town.

Then,

EASY

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

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

and

A \subseteq B,

then the number of elements in

(A \cup B)

is equal to

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of 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:

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

In a certain town,

25 %

families own a phone,

15 %

families own a car,

65 %

families own neither a phone nor a car and

2000

families own both a car and a phone. Consider the following Statements

(S) :

(S_{1}) :

35 %

families own at least one of a car or a phone.

(S_{2}) :

40, 000

families live in the town.
Then:

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of Sets

For any three sets

A, B

and

C

the set

(A \cup B \cup C) \cap {(A \cap B^{'} \cap C^{'})}^{'} \cap C^{'}

is equal to

HARD

Mathematics>Algebra>Set Theory and Relations>Algebra of 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

EASY

Mathematics>Algebra>Set Theory and Relations>Algebra of 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^{'}) =

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of 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:

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Algebra of 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:

Subject	No. of students
Mathematics	$100$
Physics	$70$
Chemistry	$46$
Mathematics and Physics	$30$
Mathematics and Chemistry	$28$
Physics and Chemistry	$23$
Mathematics, Physics and Chemistry	$18$

Important Questions on Set Theory and Relations

Learn and Prepare for any exam you want !