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

If U = 0 , 1 , 2 , 3 , 4 and A = 1 , 4 , B = 1 , 3 show that A ∪ B ' = A ' ∩ B '

Given that, If U = 0 , 1 , 2 , 3 , 4 and A = 1 , 4 , B = 1 , 3 Then, A ∪ B = 1 , 3 , 4 A ∪ B ' = 0 , 2 ..................(i) Now, A ' = 0 , 2 , 3 and B ' = 0 , 2 , 4 A ' ∩ B ' = 0 , 2 .......................(ii) From (i) and (ii) we get, A ∪ B ' = A ' ∩ B ' Hence, proved.

HARD

Earn 100

Find which are/ is the statement (s) false about complement of a set?

$a .$ The set and its complement are always universal sets.

$b .$ The complement of a universal set is the empty set.

$c .$ The complement of the empty set is a universal set.

50% studentsanswered this correctly

Important Questions on Theory of Sets

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on 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,

EASY

Mathematics>Algebra>Theory of Sets>Operations on 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 :

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on 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 :

EASY

Mathematics>Algebra>Theory of Sets>Operations on 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>Theory of Sets>Operations on Sets

Let

U

be the universal set,

A

and

B

are the subsets of

U

. If

n (U) = 650, n (A) = 310

n (A \cap B) = 95

and

n (B) = 190

, then

n (\bar{A} \cap \bar{B})

is equal to (

\bar{A}

and

\bar{B}

are the complement of

A

and

B

, respectively)

HARD

Mathematics>Algebra>Theory of Sets>Operations on 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?

HARD

Mathematics>Algebra>Theory of Sets>Operations on 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>Theory of Sets>Operations on 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>Theory of Sets>Operations on Sets

A \subset B,

then

A Δ B

is equal to

HARD

Mathematics>Algebra>Theory of Sets>Operations on 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

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

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

and

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

then

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on Sets

If $U = \{0, 1, 2, 3, 4\}$ and $A = \{1, 4\}$ , $B = \{1, 3\}$ show that $(A \cup B)' = A' \cap B'$

EASY

Mathematics>Algebra>Theory of Sets>Operations on 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 =

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on 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>Theory of Sets>Operations on 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^{'}) =

EASY

Mathematics>Algebra>Theory of Sets>Operations on 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:

MEDIUM

Mathematics>Algebra>Theory of Sets>Operations on 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>Theory of Sets>Operations on 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>Theory of Sets>Operations on Sets

(A \cap B')' =

___

EASY

Mathematics>Algebra>Theory of Sets>Operations on Sets

X

and

Y

are two sets, then

X \cap (Y \cup X)^{'}

equals

Find which are/ is the statement (s) false about complement of a set? a. The set and its complement are always universal sets. b. The complement of a universal set is the empty set. c. The complement of the empty set is a universal set.

Important Questions on Theory of Sets

Learn and Prepare for any exam you want !

Find which are/ is the statement (s) false about complement of a set?

$a .$ The set and its complement are always universal sets.

$b .$ The complement of a universal set is the empty set.

$c .$ The complement of the empty set is a universal set.