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 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

HARD

JEE Main

IMPORTANT

Earn 100

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 :

19.23% studentsanswered this correctly

Important Questions on Set Theory and Relations

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 5 September 2020 Shift 1>Q 17

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:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 6 September 2020 Shift 1>Q 18

Set

A

has

m

elements and set

B

has

n

elements. If the total number of subsets of

A

112

more than the total number of subsets of

B

, then the value of

m \cdot n

is___.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 7th January 2020 Shift 2>Q 19

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

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 9th January 2020 Shift 2>Q 20

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

and

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

then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 9th April 2019 Shift 2>Q 21

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:

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 :

Let ∪i=150Xi=∪i=1nYi=T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi's and exactly 6 of sets Yi's then n is equal to :

Important Questions on Set Theory and Relations

Learn and Prepare for any exam you want !

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 :