Verify A ⊂ B for the sets A = a , b , c , B = 1 , a , b , c , 2 . If not justify your answer.

The set A = a , b , c means that A is the set containing the data a , b , c as its elements. The definition of A ⊂ B means that whenever a is an element of A , we have that a is also an element of B . So by taking every element of the set A we see that it is an element of B . ∴ A ⊂ B Hence, verified.

EASY

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Which of the following is a singleton set?

50% studentsanswered this correctly

Important Questions on Sets, Relations and Functions

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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>Sets, Relations and Functions>Sets and Relations

In an examination

51 %

students fail in English and

45 %

fail in Maths. If

21 %

students fail in both the subjects, then

169

students pass the examination. What is the total number of students taking the exam?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The set of cubes of natural numbers is

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A = {x | x \in N, x

is a prime number less than

12}

and

B = {x |

x \in N

x

is factor of

10}

, then

A \cap B

=

…

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

Question Image

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A survey shows that

63 %

of the people in a city read newspaper

A

whereas

76 %

read news paper

B

. If

x %

of the people read both the newspapers, then a possible value of

x

can be:

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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 __________

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

X = (4^{n} - 3 n - 1 : n \in N)

and

Y = \{9 (n - 1) : n \in N\}

, then

X \cap Y =

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

In a group of boys,

25

play volleyball,

20

play badminton and

10

boys play cricket. Five boys play all the three games. 8 boys play atleast two of the three games. How many of them play only one game?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Which of the following is an empty set?

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

Two finite sets have

m

and

n

elements. The number of subsets of the first set is

112

more than that of the second. The values of

m

and

n

are respectively

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

A \subset B,

then

A Δ B

is equal to

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

n (A) = 3, n (B) = 6

and

A \subseteq B,

then the number of elements in

(A \cup B)

is equal to

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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:

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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, Relations and Functions>Sets and Relations

The following Venn diagram indicates

Question Image

HARD

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

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

Which of the following is a singleton set?

Important Questions on Sets, Relations and Functions

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