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

Prove that A - B ∪ C = A - B ∩ A - C by using Venn diagrams.

Given, to prove that A - B ∪ C = A - B ∩ A - C by using Venn diagrams. LHS : The shaded portion represents A - B ∪ C . RHS : The shaded portion represents A - B . The shaded portion represents A - C . The shaded portion represents A - B ∩ A - C . LHS = RHS Hence, proved.

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

S is an infinite proper subset of R - 0

MEDIUM

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Important Questions on Set Theory

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

How many pairs of

(x, y)

can be chosen from the set

\{2, 3, 6, 8, 9\}

such that

\frac{x}{y} + \frac{y}{x} = 2, where x \neq y ?

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

A = {x : x

is a letter of the word

E X A M I N A T I O N}

, then its roster form is

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

A = \{x : x is a multiple of 7\}, B = \{x : x is a multiple of 5\} and C = \{x : x is a multiple of 35\}

, then which one of the folowing is a null set?

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

In a party of

150

persons,

75

persons take tea,

60

persons take coffee and

50

persons take milk.

15

of them take both tea and coffee, but no one taking milk takes tea. If each person in the party takes at least one drink, then what is the number of persons taking milk only?

EASY

Mathematics>Algebra>Set Theory>Basics 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>Set Theory>Basics 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?

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

Which one of the following is a correct statement?

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

In an examination,

54 %

of the candidates passed in science and

42 %

failed in mathematics. If

32 %

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

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Which of the following statements is false?

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

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

Question Image

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Let

X = {x ∣ x = 2 + 4 k

, where

k = 0, 1, 2, 3, \dots 24}

.
Let

S

be a subset of

X

such that the sum of no two elements of

S

100

. What is the maximum possible number of elements in

S

HARD

Mathematics>Algebra>Set Theory>Basics 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,

HARD

Mathematics>Algebra>Set Theory>Basics 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?

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Which one of the following is a set of solution of the equation

x^{\sqrt{x}} = \sqrt[n]{x^{x}}

n

is a positive integer?

MEDIUM

Mathematics>Algebra>Set Theory>Basics 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

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Write

A = {3, 9, 27, 81}

in set builder form.

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Prove that

A - (B \cup C) = (A - B) \cap (A - C)

by using Venn diagrams.

EASY

Mathematics>Algebra>Set Theory>Basics of Sets

In a class, students are assigned roll numbers from I to

140

. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by

5

opted for football, and all those whose roll numbers are divisible by

3

opted for basketball. The number of students who did not opt for any of the three sports is

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

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

MEDIUM

Mathematics>Algebra>Set Theory>Basics of Sets

Let

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

then

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Important Questions on Set Theory

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