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 N denote the set of all natural numbers. Define two binary relations on N as R 1 = x , y ∈ N × N : 2 x + y = 10 and R 2 = x , y ∈ N × N : x + 2 y = 10 . Then

both R 1 and R 2 are transitive relations

both R 1 and R 2 are symmetric relations

Let P S denote the power set of S = 1 , 2 , 3 , … , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A ∩ B c ∪ B ∩ A c = ϕ and A R 2 B if A ∪ B c = B ∪ A c , ∀ A , B ∈ P S . Then :

both R 1 and R 2 are equivalence relations

only R 1 is an equivalence relation

only R 2 is an equivalence relation

both R 1 and R 2 are not equivalence relations

Let R be a relation on ℝ , given by R = { a , b : 3 a - 3 b + 7 is an irrational number } . Then R is

Reflexive but neither symmetric nor transitive

Reflexive and transitive but not symmetric

Reflexive and symmetric but not transitive

Let R be a relation on N × N defined by a , b R c , d if and only if a d b - c = b c a - d . Then R is

symmetric but neither reflexive nor transitive

transitive but neither reflexive nor symmetric

reflexive and symmetric but not transitive

symmetric and transitive but not reflexive

The relation R = a , b : g c d a , b = 1 , 2 a ≠ b , a , b ∈ ℤ is:

neither symmetric nor transitive

MEDIUM

JEE Main

IMPORTANT

Earn 100

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:

66.67% studentsanswered this correctly

Important Questions on Set Theory and Relations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 10th January 2019 Shift 1>Q 22

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:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 12th April 2019 Shift 2>Q 23

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

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 12th January 2019 Shift 1>Q 24

Let

S = \{1, 2, 3, \dots ., 100\}

, then number of non-empty subsets

A

S

such that the product of elements in

A

is even is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 12th January 2019 Shift 2>Q 25

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

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 15th April 2018>Q 26

Consider the following two binary relations on the set

A = \{a, b, c\} : R_{1} = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}

and

R_{2} = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}

, then :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 16th April 2018>Q 27

Let

N

denote the set of all natural numbers. Define two binary relations on

N

R_{1} = \{(x, y) \in N \times N : 2 x + y = 10\}

and

R_{2} = \{(x, y) \in N \times N : x + 2 y = 10\}

. Then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 10th April 2015>Q 28

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,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 4th April 2015>Q 29

Let

A

and

B

be two sets containing four and two elements respectively. Then the number of subsets of the set

A \times B

, each having at least three elements is

Important Questions on Set Theory and Relations

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