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

Let A , B and C be sets such that ϕ ≠ A ∩ B ⊆ C . Then which of the following statements is not true?

If ( A - C ) ⊆ B , then A ⊆ B

( C ∪ A ) ∩ ( C ∪ B ) = C

If ( A - B ) ⊆ C , then A ⊆ C

EASY

Earn 100

If $ℚ$ is the set of rational numbers and $ℚ^{'}$ is the set of irrational numbers. Then the set $ℚ \cup ℚ^{'}$ is closed under the operation of addition.

50% studentsanswered this correctly

Important Questions on Sets

HARD

Mathematics>Algebra>Sets>Laws of 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

EASY

Mathematics>Algebra>Sets>Laws of 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>Sets>Laws of 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,

MEDIUM

Mathematics>Algebra>Sets>Laws of 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 $S_{1} \cap S_{2} \cap S_{3}$

EASY

Mathematics>Algebra>Sets>Laws of 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

=

…

MEDIUM

Mathematics>Algebra>Sets>Laws of 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>Sets>Laws of Operations on 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?

EASY

Mathematics>Algebra>Sets>Laws of Operations on Sets

A \subset B,

then

A Δ B

is equal to

MEDIUM

Mathematics>Algebra>Sets>Laws of Operations on Sets

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

and

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

then

EASY

Mathematics>Algebra>Sets>Laws of Operations on Sets

Let

A, B, C

and

D

be four non-empty sets. The contrapositive statement of “If

A \subseteq B

and

B \subseteq D

, then

A \subseteq C

” is

MEDIUM

Mathematics>Algebra>Sets>Laws of Operations on 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,

MEDIUM

Mathematics>Algebra>Sets>Laws of 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:

HARD

Mathematics>Algebra>Sets>Laws of Operations on Sets

Let

A, B

and

C

be sets such that

ϕ \neq A \cap B \subseteq C .

Then which of the following statements is not true?

HARD

Mathematics>Algebra>Sets>Laws of Operations on 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

EASY

Mathematics>Algebra>Sets>Laws of 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^{'}) =

EASY

Mathematics>Algebra>Sets>Laws of 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

HARD

Mathematics>Algebra>Sets>Laws of 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 :

MEDIUM

Mathematics>Algebra>Sets>Laws of 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>Sets>Laws of 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>Sets>Laws of 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 ℚ is the set of rational numbers and ℚ' is the set of irrational numbers. Then the set ℚ∪ℚ' is closed under the operation of addition.

Important Questions on Sets

Learn and Prepare for any exam you want !

If $ℚ$ is the set of rational numbers and $ℚ^{'}$ is the set of irrational numbers. Then the set $ℚ \cup ℚ^{'}$ is closed under the operation of addition.