Cardinality of Sets

Q.

If A is a subset of B, then A - B is ___.

1. A

2. B

3. a null set

4. a singleton set

Q. Write all the subsets of A = {a, b}.

Q. A = {1, 3, 2, 7} then write any three subsets of A.

Q.

If A has 3 elements and P(A) denotes the power set of A, then the number of elements in P(P(A)) is

1. 8

2. 256

3. 81

4. 9

Q. If X = {1, 3, 5, 7}, then find n(X).

Q. Let A={a(1) a(2) a(3) a(4)} where a(1)>a(2)>a(3)>a(4) The total number of unordered pairs of disjoint subsets of A is equal to

Q. Suppose $A_1,A_2,....,A_{30}$ are thirty sets, each having 5 elements and $B_1,B_2,.....,B_n$ are n sets, each with 3 elements.
Let ${\bigcup }_{i=1}^{30}{A}_i={\bigcup }_{i=1}^n{B}_j=S$. Each element of S belongs to exactly 10 of the $A_{i}s$ and exactly 9 of the $B_{i}s$. Then n is equal to

1. 45
2. 50
3. 15
4. 3

Q. Find the cardinality of the set $A=\left\{\right(x:x=5n,n\in W,n<4\}$.

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $(A\cup B)$?

1. 3

2. 6

3. 9

4. 18

Q. Find the cardinal number of the following sets:

(i) A = {1, 2, 3, 4, 5, 7, 9, 11}
(ii) M = {p, q, r, s, t, u}

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $A\cup B$

1. 3

2. 6

3. 9

4. 18

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $(A\cup B)$

1. 3

2. 6

3. 9

4. 18

Q. Find the cardinal number of the following sets:

(i) A = {1, 2, 3, 4, 5, 7, 9, 11}
(ii) M = {p, q, r, s, t, u}

Q. If A = {x: x = 2n+1, n ∈ N and 3 ≤ n ≤ 9}, then the cardinality of A is .

1. 6
2. 3
3. 7
4. 9

Q. Match the sets in the roster form with the description given.

1. {2, 4, 6, 8}
2. {1, 2, 3, 4, 6, 12}
3. {2, 3, 5, 7}
4. {2, 3}

Q. The cardinality of the set A={letters of the word BANGALORE} is .

1. 8
2. 9
3. not defined

Q. The number of elements in the set {x : x is a letter of the word 'MISSISSIPPI'}, is .

1. 6
2. 4
3. 11
4. 10

Q.

If A and B are disjoint sets then,

n(A U B) = ____.

1. n(A) + n(B)

2. n(A) - n(B)

3. n(A) + n(B) - n(AB)

4. phi

Q. If $2P(5,3)=P(n,4)$ find $n$

Q. Let $U$ be the set of all triangles in a plane. If $A$ is the set of all triangles with at least one angle different from ${60}^{\circ }$, what is $A^{\prime }$ ?

1. $A^{\prime }$ is the set of all isosceles triangles.
2. $A^{\prime }$ is the set of all right-angled triangles.
3. $A^{\prime }$ is the set of all acute angle triangles.
4. $A^{\prime }$ is the set of all equilateral triangles.

Q.

If A is a subset of B, then A ⋃ B ___.

1. equals A

2. equals B

3. equals phi

4. is a subset of A

Q. How many $4$-letter words, with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

1. $5040$
2. $2500$
3. $1000$
4. $2060$

Q. If A = {x: x = 2n+1, n ∈ N and 3 ≤ n ≤ 9}, then the cardinality of A is .

1. 6
2. 9
3. 7
4. 3

Q.

1. R S P Q
2. P Q S R
3. Q S P R
4. Q R P S

Q.

A is a subset of B. If n(A) = 10 and n(B) = 30, then n(B U A) = __________ .

1. 10

2. 20

3. 30

4. 40

Q. If P = { x | x is a multiple of 10 } and
Q = { x | the unit’s (ones place )digit of x is not zero} then P ∩ Q is equal to .

1. P ∩ $\varphi$
2. P ∩ P
3. P