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

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Two finite sets $A$ and $B$ have $m$ and $n$ elements respectively. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$ , then the value of $m$ is

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Important Questions on Set Theory and Relations

HARD

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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 :

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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>Set Theory and Relations>Subsets and Power Set

A

and

B

are two non-empty finite sets having

3

and

4

elements respectively, then what would be the possible number of subsets of

A \times B ?

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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

and

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

, then

X \cap Y =

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

A = \{1, 2, 3, \dots \dots 10\}

then number of subsets of

A

containing only odd numbers is

HARD

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

There is a set

P

of ordered pairs in which each pair has a vowel as first element and a consonant as second element. It is given that

M = 4^{10} .

How many elements will be there in power set of

P

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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>Set Theory and Relations>Subsets and Power Set

If a set

A

has

4

elements, then the total number of proper subsets of set

A

, is

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

The number of proper subsets of a set having

n + 1

elentents is

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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___.

HARD

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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

HARD

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

A positive integer

k

is said to be good if there exists a partition of

\{1, 2, 3, \dots ., 20\}

into disjoint proper subsets such that the sum of the numbers in each subset of the partition is

k .

How many good numbers are there?

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

Two finite sets have

m

and

n

elements. The total number of subsets of the first set is

48

more than the total number of subsets of the second. The values of

m

and

n

respectively, are

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

Let

A

and

B

be two finite sets such that there are exactly

144

sets which are subsets of

A

or subsets of

B .

Find the number of elements in

A \cup B .

HARD

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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>Set Theory and Relations>Subsets and Power Set

Let

A = \{1, 2, 3, 4, 5, 6, 7\}

and

B = \{3, 6, 7, 9\}

. Then the number of elements in the set

\{C \subseteq A : C \cap B \neq ϕ\}

is ______

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

The total number of subsets of the set

{1, 2, \dots \dots, 10}

which do not contain the element

6

EASY

Mathematics>Algebra>Set Theory and Relations>Subsets and Power Set

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>Set Theory and Relations>Subsets and Power Set

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 :

Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is

Important Questions on Set Theory and Relations

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Two finite sets $A$ and $B$ have $m$ and $n$ elements respectively. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$ , then the value of $m$ is