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

EASY

Earn 100

Sets $B = \{0, 3, 5, 7, 9\}; A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}$

$B$ is proper subsets of the set $A$ .

50% studentsanswered this correctly

Important Questions on Sets

EASY

Mathematics>Algebra>Sets>Subsets of Sets

On the set of positive rationals, a binary operation

*

is defined by

a * b = \frac{2 a b}{5} .

2 * x = 3^{- 1}

then

x =

HARD

Mathematics>Algebra>Sets>Subsets 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>Sets>Subsets of Sets

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

and

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

then

EASY

Mathematics>Algebra>Sets>Subsets of Sets

A \subset B,

then

A Δ B

is equal to

HARD

Mathematics>Algebra>Sets>Subsets 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>Sets>Subsets of Sets

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>Subsets of Sets

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

=

…

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

Consider the two sets:

A = {m \in R :

both the roots of

x^{2} - (m + 1) x + m + 4 = 0

are real

}

and

B = [- 3, 5)

Which of the following is not true?

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

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,

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

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:

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

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:

EASY

Mathematics>Algebra>Sets>Subsets of Sets

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>Subsets of Sets

U

is the universal set with

100

elements;

A

and

B

are two sets such that

n (A) = 50, n (B) = 60

n (A \cap B) = 20

then

n (A^{'} \cap B^{'}) =

HARD

Mathematics>Algebra>Sets>Subsets of Sets

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 :

HARD

Mathematics>Algebra>Sets>Subsets of Sets

In a certain town,

25 %

families own a phone,

15 %

families 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 Statements

(S) :

(S_{1}) :

35 %

families own at least one of a car or a phone.

(S_{2}) :

40, 000

families live in the town.
Then:

EASY

Mathematics>Algebra>Sets>Subsets of Sets

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

and

A \subseteq B,

then the number of elements in

(A \cup B)

is equal to

MEDIUM

Mathematics>Algebra>Sets>Subsets of Sets

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:

EASY

Mathematics>Algebra>Sets>Subsets of Sets

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

Mathematics>Algebra>Sets>Subsets of Sets

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

Sets B=0,3,5,7,9; A=1,3,5,7,9,11,13,15,17 B is proper subsets of the set A.

Important Questions on Sets

Learn and Prepare for any exam you want !

Sets $B = \{0, 3, 5, 7, 9\}; A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}$

$B$ is proper subsets of the set $A$ .