Mathematics>Algebra>Sets>Types of Sets

EASY

Earn 100

Equal sets are always ______.

87.5% studentsanswered this correctly

Important Questions on Sets

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

An investigator interviewed

100

students to determine the performance of three drinks milk, coffee and tea. The investigator reported that

10

students take all three drinks milk, coffee and tea;

20

students take milk and coffee,

30

students take coffee and tea,

25

students take milk and tea,

12

students take milk only,

5

students take coffee only and

8

students take tea only. Then the number of students who did not take any of the three drinks is

HARD

Mathematics>Algebra>Sets>Types of 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>Types of Sets

Let $A$ be the set of vectors $a = (a_{1}, a_{2}, a_{3})$ satisfying ${(\sum_{i = 1}^{3} \frac{a_{i}}{2^{i}})}^{2} = \sum_{i = 1}^{3} \frac{a_{i}^{2}}{2^{i}}$ . Then,

EASY

Mathematics>Algebra>Sets>Types of Sets

If

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

EASY

Mathematics>Algebra>Sets>Types of Sets

Let

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} .

Then the number of subsets of

A

containing two or three elements is

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

If

A = \{(a_{1}, a_{2}, \dots . a_{10}) : a_{1} \in {1, 2, 3}, a_{1} + a_{i + 1}

is even,

1 \leq i \leq 9\},

then the number of elements in the set

A

is

MEDIUM

Mathematics>Algebra>Sets>Types of Sets

Let

S = \{x \in R : \cos (x) + \cos (\sqrt{2} x) < 2\},

then

EASY

Mathematics>Algebra>Sets>Types of Sets

A

set

T

is given as

T = \{x \in R ∣ (x - 3) = (x + 4)^{2}, x < 2\} .

Which of these would be TRUE about the set

T ?

EASY

Mathematics>Algebra>Sets>Types of Sets

The set of cubes of natural numbers is

EASY

Mathematics>Algebra>Sets>Types of Sets

Two finite sets respectively have

x

and

y

number of elements. The total number of sub sets of the first is

56

more than the total no. of sub sets of the second. The value of

x, y

are respectively __________

EASY

Mathematics>Algebra>Sets>Types of Sets

Verify

A \subset B

for the sets

A = \{a, b, c\}, B = \{1, \{a, b, c\}, 2\}

. If not justify your answer.

EASY

Mathematics>Algebra>Sets>Types of Sets

Which of the following is an empty set?

EASY

Mathematics>Algebra>Sets>Types of Sets

The following Venn diagram indicates

Question Image

HARD

Mathematics>Algebra>Sets>Types of Sets

Let

a > 0, a \neq 1

. Then, the set

S

of all positive real numbers

b

satisfying

(1 + a^{2}) (1 + b^{2}) = 4 a b

is

EASY

Mathematics>Algebra>Sets>Types of Sets

Whether the given set is finite or infinite

The set of prime numbers less than $99$ .

EASY

Mathematics>Algebra>Sets>Types of Sets

Whether the given statement is example of the null set or not
Set of even prime numbers

EASY

Mathematics>Algebra>Sets>Types of Sets

Whether the given set is finite or infinite
The set of positive integers greater than

100

EASY

Mathematics>Algebra>Sets>Types of Sets

Whether the following set is finite or infinite:

The set of lines which are parallel to the $x$ -axis.

EASY

Mathematics>Algebra>Sets>Types of Sets

The sets

\{a, e, i, o, u\}

and

\{c, d, e, f\}

are disjoint or not.

EASY

Mathematics>Algebra>Sets>Types of Sets

Whether the given statement is example of the null set or not
Set of odd natural numbers divisible by

2