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

Let S = x ∈ R : cos x + cos 2 x < 2 , then

S is an infinite proper subset of R - 0

EASY

Earn 100

Which of the following is an empty set ?

50% studentsanswered this correctly

Important Questions on Set Theory

HARD

Mathematics>Algebra>Set Theory>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?

EASY

Mathematics>Algebra>Set Theory>Types of Sets

In the given Venn diagram $n (A)$ is

Question Image

EASY

Mathematics>Algebra>Set Theory>Types of Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

MEDIUM

Mathematics>Algebra>Set Theory>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

EASY

Mathematics>Algebra>Set Theory>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

HARD

Mathematics>Algebra>Set Theory>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>Set Theory>Types of Sets

The number of items in the set

A

40

, in the Set

B

32

; in the Set

C

50

; in both

A

and

B

4

; in both

A

and

C

5

; in both

B

and

C

7

; in all the set is

2

. How many are in only one set?

HARD

Mathematics>Algebra>Set Theory>Types of Sets

Let

Z

be the set of integers. If

A = \{x \in Z : 2^{(x + 2) (x^{2} - 5 x + 6)} = 1\}

and

B = {x \in Z : - 3 < 2 x - 1 < 9}

, then the number of subsets of the set

A \times B

, is :

EASY

Mathematics>Algebra>Set Theory>Types of Sets

The set of cubes of natural numbers is

EASY

Mathematics>Algebra>Set Theory>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>Set Theory>Types of Sets

A

set

T

is given as

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