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.

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

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Empty set is also known as set.

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Important Questions on Theory of Sets

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

Give one example for a finite set and an infinite set.

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

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

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

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?

EASY

Mathematics>Algebra>Theory of Sets>Types 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 :

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

The set of cubes of natural numbers is

HARD

Mathematics>Algebra>Theory of Sets>Types 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

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

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

Question Image

EASY

Mathematics>Algebra>Theory of Sets>Types 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>Theory of Sets>Types of Sets

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 __________

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

Verify

A \subset B

for the sets

A = \{a, b, c\}, B = \{1, \{a, b, c\}, 2\}

. If not justify your answer.

HARD

Mathematics>Algebra>Theory of Sets>Types 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>Theory of Sets>Types of Sets

Which of the following is an empty set?

MEDIUM

Mathematics>Algebra>Theory of Sets>Types 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 :

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

A

and

B

are disjoint sets, then

B \cap A^{'}

, where

A^{'}

is complement of

A

, is equal to

HARD

Mathematics>Algebra>Theory of Sets>Types 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?

EASY

Mathematics>Algebra>Theory of Sets>Types of Sets

If the total number of

m

-element subsets of the set

A = \{a_{1}, a_{2}, \dots, a_{n}\}

k

times the number of

m

element subsets containing

a_{4}

, then

n

MEDIUM

Mathematics>Algebra>Theory of Sets>Types of Sets

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___.

MEDIUM

Mathematics>Algebra>Theory of Sets>Types of Sets

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>Theory of Sets>Types of Sets

The following Venn diagram indicates

Question Image

HARD

Mathematics>Algebra>Theory of Sets>Types of Sets

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

Empty set is also known as set.

Important Questions on Theory of Sets

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